[seqfan] A261332 and Number of n - almost primes in the interval [3^n, 5^n]

[zak seidov]

Consider sequence
S1 Number of n-AP in the interval [3^n,5^n] inclusive.2, 7, 26, 83, 256, 766, 2211, 6277, 17424, 47743
Mma Table[c = 0; Do[If[PrimeOmega[k] == n, c++], {k, 3^n, 5^n}]; c, {n, 10}]
and
A261332  Expansion of Product_{k>=1} (1+x^k)^(A002203(k)).         1, 2, 7, 26, 83, 278, 894, 2848, 8947, 27844, 85774, 262090 
Terms {2, 7, 26, 83} are in both - is it just coincidence?

Thx,
Zak