The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A347156 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A347156

Sum of squares of distinct prime divisors of n that are < sqrt(n).
(history; published version)

#5 by Susanna Cuyler at Fri Aug 20 22:52:18 EDT 2021

STATUS

proposed

approved

#4 by Ilya Gutkovskiy at Fri Aug 20 12:28:56 EDT 2021

STATUS

editing

proposed

#3 by Ilya Gutkovskiy at Fri Aug 20 11:21:16 EDT 2021

CROSSREFS

Cf. A001157, A005063, A005066, A098002, A333806, A333808, A339353, A347157, A347158.

#2 by Ilya Gutkovskiy at Fri Aug 20 11:13:59 EDT 2021

NAME

allocated for Ilya GutkovskiySum of squares of distinct prime divisors of n that are < sqrt(n).

DATA

0, 0, 0, 0, 0, 4, 0, 4, 0, 4, 0, 13, 0, 4, 9, 4, 0, 13, 0, 4, 9, 4, 0, 13, 0, 4, 9, 4, 0, 38, 0, 4, 9, 4, 25, 13, 0, 4, 9, 29, 0, 13, 0, 4, 34, 4, 0, 13, 0, 29, 9, 4, 0, 13, 25, 53, 9, 4, 0, 38, 0, 4, 58, 4, 25, 13, 0, 4, 9, 78, 0, 13, 0, 4, 34, 4, 49, 13, 0, 29

OFFSET

1,6

FORMULA

G.f.: Sum_{k>=1} prime(k)^2 * x^(prime(k)*(prime(k) + 1)) / (1 - x^prime(k)).

MATHEMATICA

Table[DivisorSum[n, #^2 &, # < Sqrt[n] && PrimeQ[#] &], {n, 1, 80}]

nmax = 80; CoefficientList[Series[Sum[Prime[k]^2 x^(Prime[k] (Prime[k] + 1))/(1 - x^Prime[k]), {k, 1, nmax}], {x, 0, nmax}], x] // Rest

CROSSREFS

Cf. A001157, A005063, A005066, A098002, A333806, A333808, A339353.

KEYWORD

allocated

nonn

AUTHOR

Ilya Gutkovskiy, Aug 20 2021

STATUS

approved

editing

#1 by Ilya Gutkovskiy at Fri Aug 20 11:13:59 EDT 2021

NAME

allocated for Ilya Gutkovskiy

KEYWORD

allocated

STATUS

approved