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A136135 Sum of squares until integer log : sopfr(n). Or also, s(s+1)(2s+1)/6 where s=sopfr(n). 0

%I #9 Nov 22 2021 10:11:59

%S 0,5,14,30,55,55,140,91,91,140,506,140,819,285,204,204,1785,204,2470,

%T 285,385,819,4324,285,385,1240,285,506,8555,385,10416,385,1015,2470,

%U 650,385,17575,3311,1496,506,23821,650,27434,1240,506,5525,35720,506,1015

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

%C 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).

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

%Y Cf. A074374, A001414.

%K nonn

%O 0,2

%A _Carlos Alves_, Dec 16 2007

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Last modified July 13 23:31 EDT 2024. Contains 374290 sequences. (Running on oeis4.)