A345299 a(n) = Sum_{p|n} p^pi(p).

0, 2, 9, 2, 125, 11, 2401, 2, 9, 127, 161051, 11, 4826809, 2403, 134, 2, 410338673, 11, 16983563041, 127, 2410, 161053, 1801152661463, 11, 125, 4826811, 9, 2403, 420707233300201, 136, 25408476896404831, 2, 161060, 410338675, 2526, 11, 6582952005840035281, 16983563043

Offset

1,2

Links

Table of n, a(n) for n=1..38.

Formula

a(p) = p^pi(p) for p prime.

Example

a(10) = Sum_{p|10} p^pi(p) = 2^1 + 5^3 = 127.

Mathematica

Table[Sum[k^PrimePi[k] (PrimePi[k] - PrimePi[k - 1]) (1 - Ceiling[n/k] + Floor[n/k]), {k, n}], {n, 50}]

Prog

(Python)
from sympy import primefactors, primepi
def A345299(n): return sum(p**primepi(p) for p in primefactors(n)) # Chai Wah Wu, Jun 13 2021

Crossrefs

Cf. A000720, A066328.

Sequence in context: A248433 A091943 A318511 * A276048 A339203 A179451

Adjacent sequences: A345296 A345297 A345298 * A345300 A345301 A345302

Keyword

nonn

Author

Wesley Ivan Hurt, Jun 13 2021

Status

approved