what is the value "60" doing in A000028 ??

[Meeussen Wouter (bkarnd)]

ID Number: A000028 (Formerly M0520 and N0187) Sequence:
2,3,4,5,7,9,11,13,16,17,19,23,24,25,29,30,31,37,40,41,42,43,
47,49,53,54,56,59,60,61,66,67,70,71,72,73,78,79,81,83,84,88,
89,90,96,97,101,102,103,104,105,107,108,109,110,113 Name: A 2-way
classification of integers: a(n) is smallest number not of form a(i)a(j),
i<j<n.

2*30 =60 , no?  
I must be goofing angain ! Low A-numbers have been checked & double checked
umpteen times.

I find:
 
Do[it= Union[it,{Min[Complement[Complement[Range[2,2k+2],it],
Flatten[Outer[If[#1=!=#2,Times[#1,#2],1]&,it,it,1]]]]}],{k,3,160}];it

 
{2, 3, 4, 5, 7, 9, 11, 13, 16, 17, 19, 23, 24, 25, 29, 30, 31, 37, 40, 41, \
42, 43, 47, 49, 53, 54, 56, 59, 61, 66, 67, 70, 71, 73, 78, 79, 81, 83, 88,
\
89, 97, 101, 102, 103, 104, 105, 107, 109, 110, 113, 114, 121, 127, 128,
130, \
131, 135, 136, 137, 138, 139, 149, 151, 152, 154, 157, 163, 165, 167, 169, \
170, 173, 174, 179, 180, 181, 182, 184, 186, 189, 190, 191, 192, 193, 195, \
197, 199, 211, 222, 223, 227, 229, 230, 231, 232, 233, 238, 239, 240, 241, \
246, 248, 250, 251, 252, 255, 257, 258, 263, 266, 269, 271, 273, 277, 281, \
282, 283, 285, 286, 288, 289, 290, 293, 296, 297, 300, 307, 310, 311, 313, \
317, 318, 320,  ....

This sequence and its companion \ complement :
ID Number: A000379 (Formerly M4065 and N1685) Sequence:
1,6,8,10,12,14,15,18,20,21,22,26,27,28 ...

seem to differ in the number of divisors their elements have:
A000028 : can have {2, 3, 5, 8, 14, 18, 20, ...  divisors, while
A000379 : can have {1, 4, 6, 7, 9, 10, 12, 15, 16 .. divisors.

I'll leave the link with the infinitary divisors for later,

cheers,

Wouter Meeussen
tel  +32 (0)51 332 124
fax +32 (0)51 332 175
mail: wouter.meeussen at vandemoortele.com





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