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A359362
a(n) = (A001222(n) + 1) * A056239(n), where A001222 counts prime indices and A056239 adds them up.
5
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.
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.
Sequence in context: A049066 A151688 A159276 * A056942 A115947 A247653
KEYWORD
nonn
AUTHOR
Gus Wiseman, Dec 31 2022
STATUS
approved