A353065 - OEIS

%I #8 Apr 21 2022 16:01:11

%S 1,3,11,32,92,239,608,1465,3450,7858,17525,38165,81653,171497,354785,

%T 723084,1454642,2889854,5676607,11031046,21224439,40453596,76428636,

%U 143192339,266172016,491072611,899583306,1636775949,2958900040,5316004485,9494514599

%N Euler transform of odd primes.

%F G.f.: Product_{k>=1} 1 / (1 - x^k)^prime(k+1).

%p a:= proc(n) option remember; `if`(n=0, 1, add(a(n-j)*add(

%p       d*ithprime(d+1), d=numtheory[divisors](j)), j=1..n)/n)

%p     end:

%p seq(a(n), n=0..30);  # _Alois P. Heinz_, Apr 21 2022

%t nmax = 30; CoefficientList[Series[Product[1/(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[d Prime[d + 1], {d, Divisors[k]}] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 30}]

%Y Cf. A005380, A030009, A030012, A065091.

%K nonn

%O 0,2

%A _Ilya Gutkovskiy_, Apr 21 2022