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A347156 Sum of squares of distinct prime divisors of n that are < sqrt(n). 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,6
LINKS
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
Sequence in context: A010675 A035673 A035638 * A292142 A345450 A098002
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Aug 20 2021
STATUS
approved

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Last modified March 28 03:28 EDT 2024. Contains 371235 sequences. (Running on oeis4.)