A359362 a(n) = (A001222(n) + 1) * A056239(n), where A001222 counts prime indices and A056239 adds them up.

0, 2, 4, 6, 6, 9, 8, 12, 12, 12, 10, 16, 12, 15, 15, 20, 14, 20, 16, 20, 18, 18, 18, 25, 18, 21, 24, 24, 20, 24, 22, 30, 21, 24, 21, 30, 24, 27, 24, 30, 26, 28, 28, 28, 28, 30, 30, 36, 24, 28, 27, 32, 32, 35, 24, 35, 30, 33, 34, 35, 36, 36, 32, 42, 27, 32, 38

Offset

1,2

Comments

A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798.

Links

Table of n, a(n) for n=1..67.

Formula

a(n) = (k + 1) * m, where m and k are the sum and length of the integer partition with Heinz number n.

a(n) = 2*A304818(n) - A261079(n).

Mathematica

primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
Table[(PrimeOmega[n]+1)*Total[primeMS[n]], {n, 30}]

Prog

(Python)
from sympy import primepi, factorint
def A359362(n): return (sum((f:=factorint(n)).values())+1)*sum(primepi(p)*e for p, e in f.items()) # Chai Wah Wu, Jan 01 2023

Crossrefs

A055396 gives minimum prime index, maximum A061395.

A112798 list prime indices, length A001222, sum A056239.

Cf. A261079, A316413, A326836, A326837, A326844, A326846, A359358.

Sequence in context: A049066 A151688 A159276 * A056942 A115947 A247653

Adjacent sequences: A359359 A359360 A359361 * A359363 A359364 A359365

Keyword

nonn

Author

Gus Wiseman, Dec 31 2022

Status

approved