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

1,5

Links

Andrew Howroyd, Table of n, a(n) for n = 1..10000

Example

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

Mathematica

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

Prog

(PARI) a(n) = { my(f=factor(n)); prod(i=1, #f~, my([p, e]=f[i, ]); primepi(primepi(p))^e) } \\ Andrew Howroyd, Nov 10 2025

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.

Sequence in context: A126211 A095414 A339012 * A328766 A219203 A341981

Adjacent sequences: A357981 A357982 A357983 * A357985 A357986 A357987

Keyword

nonn,mult,easy

Author

Gus Wiseman, Oct 25 2022

Status

approved