A136135 Sum of squares until integer log : sopfr(n). Or also, s(s+1)(2s+1)/6 where s=sopfr(n).

0, 5, 14, 30, 55, 55, 140, 91, 91, 140, 506, 140, 819, 285, 204, 204, 1785, 204, 2470, 285, 385, 819, 4324, 285, 385, 1240, 285, 506, 8555, 385, 10416, 385, 1015, 2470, 650, 385, 17575, 3311, 1496, 506, 23821, 650, 27434, 1240, 506, 5525, 35720, 506, 1015

Offset

0,2

Comments

Sequence A074374 is similar, based on the triangular numbers, giving s(s+1)/2 with s=sopfr(n). Here it is based on the square pyramidal numbers, giving s(s+1)(2s+1)/6 with s=sopfr(n).

Links

Table of n, a(n) for n=0..48.

Mathematica

sopfr = Function[x, Plus @@ Map[Times @@ # &, FactorInteger[x]]]; Map[ #(# + 1)(2# + 1)/6 &, sopfr /@ Range[130]]

Crossrefs

Cf. A074374, A001414.

Sequence in context: A161698 A049791 A053461 * A231673 A211653 A096893

Adjacent sequences: A136132 A136133 A136134 * A136136 A136137 A136138

Keyword

nonn

Author

Carlos Alves, Dec 16 2007

Status

approved