A098002 Sum of squares of distinct prime divisors p of n, where each p <= sqrt(n).

0, 0, 0, 4, 0, 4, 0, 4, 9, 4, 0, 13, 0, 4, 9, 4, 0, 13, 0, 4, 9, 4, 0, 13, 25, 4, 9, 4, 0, 38, 0, 4, 9, 4, 25, 13, 0, 4, 9, 29, 0, 13, 0, 4, 34, 4, 0, 13, 49, 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, 9, 4, 0, 62, 25, 4, 9, 4, 0, 38, 49

Offset

1,4

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Formula

G.f.: Sum_{k>=1} prime(k)^2 * x^(prime(k)^2) / (1 - x^prime(k)). - Ilya Gutkovskiy, Aug 19 2021

Example

2 and 3 are the distinct prime divisors of 12 and both 2 and 3 are <= sqrt(12), so a(12) = 2^2 + 3^2 = 13.

Mathematica

ssdpd[n_]:=Total[Select[Transpose[FactorInteger[n]][[1]], #<=Sqrt[n]&]^2]; Join[{0}, Array[ssdpd, 90, 2]] (* Harvey P. Dale, Mar 11 2013 *)

Prog

(PARI) a(n) = sumdiv(n, d, isprime(d)*(d^2<=n)*d^2); \\ Michel Marcus, Dec 22 2017

Crossrefs

Cf. A097974.

Sequence in context: A347156 A292142 A345450 * A241658 A256719 A362209

Adjacent sequences: A097999 A098000 A098001 * A098003 A098004 A098005

Keyword

nonn

Author

Leroy Quet, Sep 08 2004

Extensions

More terms from John W. Layman, Sep 14 2004

Status

approved