A347156 Sum of squares of distinct prime divisors of n that are < sqrt(n).

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

Links

Table of n, a(n) for n=1..80.

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, A347157, A347158.

Sequence in context: A010675 A035673 A035638 * A292142 A345450 A098002

Adjacent sequences: A347153 A347154 A347155 * A347157 A347158 A347159

Keyword

nonn

Author

Ilya Gutkovskiy, Aug 20 2021

Status

approved