tau(k)/bigomega(k)

[Ralf Stephan]

Emeric,
one of your sequences caught my eyes for another reason: most
of A109428 (numbers such that omega(n) does not divide sigma(n))
consists of even numbers, and their half has overlaps with a set 
of other sequences which are interesting themselves.

I am not sure which is the best fit so I'll include all. This way
perhaps the others can be also better characterized. At the least, 
the following contains a lot of potential conjectures :)

Regards,

A109428/2:
9,18,25,36,42,49,50,72,78,81,98,100,225/2,114,121,126,273/2,144,150,162,168,169,182,186,196,399/2,200,441/2,222,234,242,258,525/2,266,288,289,312,324,651/2,338,342,350,361,366,741/2,378,777/2,392,400,402,819/2,434,438,450,903/2,456,474,484,975/2,494,

A046685 ,1,2,4,8,9,18,25,100,121,225,289,484,529,841,1089,1156,1681,2116,2209,2601,2809,3364,3481,4761,5041,6724,6889,7225,7569,7921,8836,10201,11236,11449,12769,13225,13924,15129,17161,18769,19881,20164,21025,
%N A046685 Sum of cubes of divisors of n and sum of 4th powers of divisors of n are relatively prime.

A046683 ,1,2,4,9,18,25,36,100,121,225,289,484,529,841,900,1089,1156,1681,2116,2209,2601,2809,3364,3481,4356,4761,5041,6724,6889,7225,7569,7921,8836,10201,10404,11236,11449,12769,13225,13924,15129,17161,18769,19044,
%N A046683 Sum of squares of divisors of n and sum of cubes of divisors of n are relatively prime.

A096033 ,1,2,8,9,18,25,32,49,50,72,81,98,121,128,162,169,200,225,242,288,289,338,361,392,441,450,512,529,578,625,648,722,729,800,841,882,961,968,1058,1089,1152,1225,1250,1352,1369,1458,1521,1568,1681,1682,1800,1849,
%N A096033 Difference between leg and hypotenuse in primitive Pythagorean triangles.
%F A096033 Union of A001105 (integers of form 2*n^2) and A016754 (the odd squares).

A062952 ,1,4,9,18,25,36,49,78,87,100,121,162,169,196,225,326,289,348,361,450,441,484,529,702,645,676,807,882,841,900,961,1334,1089,1156,1225,1566,1369,1444,1521,1950,1681,1764,1849,2178,2175,2116,2209,2934,2443,2580,
%F A062952 a(n) = Sum_{d|n} phi(d)*sigma(d). a(n) = Sum_{k=1..n} sigma(n/gcd(n,k)).

A086955 ,1,6,9,18,25,38,49,66,81,102,121,146,169,198,225,258,289,326,361,402,441,486,529,578,625,678,729,786,841,902,961,1026,1089,1158,1225,1298,1369,1446,1521,1602,1681,1766,1849,1938,2025,2118,2209,2306,2401,2502,
%N A086955 n^2+2n+2-(-1)^n.

A038838 ,9,18,25,27,36,45,49,50,54,63,72,75,81,90,98,99,100,108,117,121,125,126,135,144,147,150,153,162,169,171,175,180,189,196,198,200,207,216,225,234,242,243,245,250,252,261,270,275,279,288,289,294,297,300,306,
%N A038838 Divisible by square of odd prime.

A038837 ,9,18,25,27,36,45,49,50,54,72,75,81,90,98,99,100,108,121,125,135,144,147,150,153,162,169,175,180,189,196,198,200,207,216,225,242,243,245,250,261,270,279,288,289,294,297,300,306,324,325,338,343,350,351,360,
%N A038837 Solutions to HAKMEM Problem 45.

A034046 ,9,18,25,27,45,49,50,54,75,81,90,98,99,117,121,125,126,147,150,153,162,169,171,189,198,225,234,242,243,245,250,261,270,275,289,294,297,306,315,325,333,338,342,350,361,363,369,378,387,405,414,425,
%N A034046 Numbers that are both primitively and imprimitively represented by x^2+y^2+z^2.
%F A034046 Union of A034046 and A034047 is A000378. Intersection of A047449 and A034043 is A034046. Numbers that are in A000378 and neither squarefree nor congruent to 0 mod 4. - Ray Chandler (RayChandler(AT)alumni.tcu.edu), Sep 05 2004

A069562 ,9,18,25,36,49,50,72,81,98,100,121,144,162,169,196,200,225,242,288,289,324,338,361,392,400,441,450,484,529,576,578,625,648,676,722,729,784,800,841,882,900,961,968,1058,1089,1152,1156,1225,1250,1296,1352,1369,
%N A069562 sum(d|n,6d/(2+mu(d))) is odd.

A072502 ,9,18,25,36,49,50,72,98,100,121,144,169,196,200,242,288,289,338,361,392,400,484,529,576,578,676,722,784,800,841,961,968,1058,1152,1156,
%N A072502 Numbers that are run sums (trapezoidal, the difference between two triangular numbers) in exactly 3 ways.

You wrote 
> Dear Seqfans,
> Sequence A109421 gives the numbers k such that tau(k)/bigomega(k)
> is an integer [tau(k)=number of divisors of k; bigomega(k)=number
> of prime divisors of k, counted with multiplicities].