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%I #7 May 06 2022 15:13:10
%S 1,3,8,23,57,137,317,705,1524,3224,6667,13521,26980,52985,102624,
%T 196248,370849,693159,1282537,2350584,4269912,7692044,13748080,
%U 24390170,42966637,75187515,130737631,225957706,388279308,663533206,1127936772,1907676978,3210783522,5378798428
%N Expansion of Product_{k>=1} (1 + x^k)^prime(k+1).
%C Weigh transform of odd primes.
%t nmax = 33; CoefficientList[Series[Product[(1 + x^k)^Prime[k + 1], {k, 1, nmax}], {x, 0, nmax}], x]
%t 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}]
%Y Cf. A061152, A065091, A353065, A353160, A353170.
%K nonn
%O 0,2
%A _Ilya Gutkovskiy_, Apr 28 2022
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