A115003 a(n) = Sum_{k=1..n} J_4(k)/240.

4, 9, 19, 35, 62, 101, 162, 242, 361, 511, 719, 975, 1323, 1728, 2271, 2895, 3695, 4610, 5776, 7056, 8681, 10466, 12653, 15053, 18000, 21120, 24968, 29064, 33944, 39164, 45404, 51884, 59693, 67838, 77358, 87342, 99116, 111116, 125361, 140001, 156849, 174339, 194671, 215151

Offset

5,1

Comments

See A115000 for further information.

Links

Andrew Howroyd, Table of n, a(n) for n = 5..10000

Mathematica

f[p_, e_] := p^(4*e) - p^(4*e-4); s[n_] := Times @@ f @@@ FactorInteger[n]; s[1] = 1; Accumulate[Array[s, 48]][[5;; -1]] / 240 (* Amiram Eldar, Nov 24 2025 *)

Prog

(PARI) J(m, n)=my(f=factor(n)); prod(i=1, #f~, my([p, e]=f[i, ]); (p^m-1)*p^(m*(e-1)))
lista(n)={my(a=vector(n), s=0); for(n=1, #a, s+=J(4, n)/240; a[n]=s); a[5..n]} \\ Andrew Howroyd, Nov 18 2025

Crossrefs

Cf. A115000, A115002.

Sequence in context: A038405 A301245 A301103 * A210730 A008113 A008111

Adjacent sequences: A115000 A115001 A115002 * A115004 A115005 A115006

Keyword

nonn

Author

Franklin T. Adams-Watters, Dec 10 2005

Extensions

a(39) onward from Andrew Howroyd, Nov 18 2025

Status

approved