A357984 Replace prime(k) with A000720(k) in the prime factorization of n.

1, 0, 1, 0, 2, 0, 2, 0, 1, 0, 3, 0, 3, 0, 2, 0, 4, 0, 4, 0, 2, 0, 4, 0, 4, 0, 1, 0, 4, 0, 5, 0, 3, 0, 4, 0, 5, 0, 3, 0, 6, 0, 6, 0, 2, 0, 6, 0, 4, 0, 4, 0, 6, 0, 6, 0, 4, 0, 7, 0, 7, 0, 2, 0, 6, 0, 8, 0, 4, 0, 8, 0, 8, 0, 4, 0, 6, 0, 8, 0, 1, 0, 9, 0, 8, 0, 4

Offset: 1

Author

Gus Wiseman, Oct 25 2022

Keywords

• nonn
• mult

Examples

			We have 91 = prime(4) * prime(6), so a(91) = pi(4) * pi(6) = 6.
		

Crossrefs

Other multiplicative sequences: A003961, A357852, A064988, A064989, A357983.

The version for p instead of pi is A299200, horz A357977, strict A357982.

The version for nu is A355741.

The version for bigomega is A355742.

The horizontal version is A357980.

A000040 lists the prime numbers.

A000720 is PrimePi.

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

Cf. A033879, A033880, A063834, A066207, A076610, A296150, A357975.

Programs

Mathematica

primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
Table[Times@@PrimePi/@primeMS[n],{n,100}]