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%I #10 Oct 28 2022 20:53:02
%S 1,1,2,1,2,2,3,1,4,2,4,2,5,3,4,1,6,4,8,2,6,4,10,2,4,5,8,3,12,4,15,1,8,
%T 6,6,4,18,8,10,2,22,6,27,4,8,10,32,2,9,4,12,5,38,8,8,3,16,12,46,4,54,
%U 15,12,1,10,8,64,6,20,6,76,4,89,18,8,8,12,10
%N Fully multiplicative with a(prime(k)) = A000009(k+1).
%e We have 525 = prime(2)*prime(3)*prime(3)*prime(4) so a(525) = Q(3)*Q(4)*Q(4)*Q(5) = 2*2*2*3 = 24, where Q = A000009.
%t primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t ptf[f_][n_]:=Product[f[i],{i,primeMS[n]}];
%t Array[ptf[PartitionsQ[#+1]&],100]
%Y Other multiplicative sequences: A003961, A064988, A064989, A357852, A357980.
%Y The non-strict version is A003964.
%Y The unshifted horizontal version is A357978, non-strict A357977.
%Y The unshifted version is A357982.
%Y A000040 lists the primes.
%Y A056239 adds up prime indices, row-sums of A112798.
%Y Cf. A000009, A000720, A076610, A273873, A296150, A357979.
%K nonn,mult
%O 1,3
%A _Gus Wiseman_, Oct 28 2022
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