A357853 Fully multiplicative with a(prime(k)) = A000009(k+1).

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, 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, 15, 12, 1, 10, 8, 64, 6, 20, 6, 76, 4, 89, 18, 8, 8, 12, 10

Offset: 1

Author

Gus Wiseman, Oct 28 2022

Keywords

• nonn
• mult

Examples

			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.
		

Crossrefs

Other multiplicative sequences: A003961, A064988, A064989, A357852, A357980.

The non-strict version is A003964.

The unshifted horizontal version is A357978, non-strict A357977.

The unshifted version is A357982.

A000040 lists the primes.

A056239 adds up prime indices, row-sums of A112798.

Cf. A000009, A000720, A076610, A273873, A296150, A357979.

Programs

Mathematica

primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
ptf[f_][n_]:=Product[f[i],{i,primeMS[n]}];
Array[ptf[PartitionsQ[#+1]&],100]