# [seqfan] Is this right? Main diagonal A[n.n] of array A[k, n] = n-th natural number m such that m and m+2 are both divisible by exactly k primes (counted with multiplicity).

Jonathan Post jvospost3 at gmail.com
Thu Aug 12 20:05:40 CEST 2010

```3, 33, 42, 196, 750, ...?

n-th natural number m such that m and m+2 are both divisible by
exactly n primes (with multiplicity).

Is this right?  Main diagonal A[n,n]  of  A[k,n] = n-th natural number
m such that m and m+2 are both divisible by exactly k primes (counted
with multiplicity).

Row 1 = A001359 = the lesser of twin primes.
3, 5, 11, 17, 29, 41, 59, 71, 101, 107

Row 2 = A092207  = Numbers n such that n and n+2 are semiprimes. .
4, 33, 49, 55, 85, 91, 93, 119, 121, 141

Row 3 = A180117 = m and m+2 are both divisible by exactly 3 primes
(counted with multiplicity).
18,28,42,50,66,68,76,114,170,172,186,188,236,242

Row 4 = A180150 = m and m+2 are both divisible by exactly 4 primes
(counted with multiplicity).
54,88,150,196,232,248,294,306,328,340,342,348,460,488,490,568,570,664

Row 5 = A180151 = m and m+2 are both divisible by exactly 5 primes
(counted with multiplicity).
270,464,592,700,750,918,1240,1638,1648,1672

I would appreciate, if anyone is interested, checking each of the rows
as above (I see that A092207 Numbers n such that n and n+2 are
semiprimes. replaced a defective recent seq that claimed to be the
same but missed the value 49).

Then perhaps extend any row(s), add rows for k>5, and checking thr
main diagonal as I have tried to generate "by hand" from unedited
data.

```