A353169 Expansion of Product_{k>=1} (1 + x^k)^prime(k+1).

1, 3, 8, 23, 57, 137, 317, 705, 1524, 3224, 6667, 13521, 26980, 52985, 102624, 196248, 370849, 693159, 1282537, 2350584, 4269912, 7692044, 13748080, 24390170, 42966637, 75187515, 130737631, 225957706, 388279308, 663533206, 1127936772, 1907676978, 3210783522, 5378798428

Offset: 0

Author

Ilya Gutkovskiy, Apr 28 2022

Keywords

• nonn

Comments

Weigh transform of odd primes.

Crossrefs

Cf. A061152, A065091, A353065, A353160, A353170.

Programs

Mathematica

nmax = 33; CoefficientList[Series[Product[(1 + x^k)^Prime[k + 1], {k, 1, nmax}], {x, 0, nmax}], x]
a[0] = 1; a[n_] := a[n] = (1/n) Sum[Sum[(-1)^(k/d + 1) d Prime[d + 1], {d, Divisors[k]}] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 33}]