The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A361012 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A361012

Multiplicative with a(p^e) = sigma(e), where sigma = A000203.
(history; published version)

#21 by Alois P. Heinz at Tue Feb 28 09:28:00 EST 2023

STATUS

proposed

approved

#20 by Chai Wah Wu at Tue Feb 28 09:27:38 EST 2023

STATUS

editing

proposed

#19 by Chai Wah Wu at Tue Feb 28 09:27:35 EST 2023

PROG

(Python)

from math import prod

from sympy import divisor_sigma, factorint

def A361012(n): return prod(divisor_sigma(e) for e in factorint(n).values()) # Chai Wah Wu, Feb 28 2023

STATUS

approved

editing

#18 by Peter Luschny at Tue Feb 28 07:46:14 EST 2023

STATUS

reviewed

approved

#17 by Joerg Arndt at Tue Feb 28 07:44:10 EST 2023

STATUS

proposed

reviewed

#16 by Vaclav Kotesovec at Tue Feb 28 07:34:24 EST 2023

STATUS

editing

proposed

#15 by Vaclav Kotesovec at Tue Feb 28 07:33:55 EST 2023

FORMULA

Sum_{k=1..n} a(k) ~ c * n, where c = Product_{p prime} (1 + Sum_{e>=2} (sigma(e) - sigma(e-1)) / p^e) = 2.96008030202494141048182047811089469392843909592516341... = A361013

STATUS

proposed

editing

#14 by Vaclav Kotesovec at Tue Feb 28 06:59:33 EST 2023

STATUS

editing

proposed

#13 by Vaclav Kotesovec at Tue Feb 28 06:56:06 EST 2023

FORMULA

Dirichlet g.f.: Product_{primes p prime} (1 + Sum_{e>=1} sigma(e) / p^(e*s)).

#12 by Vaclav Kotesovec at Tue Feb 28 06:54:59 EST 2023

NAME

Multiplicative with a(p^e) = sigma(e), where sigma = A000203.