A344711 a(n) = Sum_{k=1..n} (A000330(n) mod k^2).

0, 1, 7, 19, 16, 50, 106, 66, 174, 233, 144, 210, 501, 277, 504, 965, 984, 893, 1566, 1946, 1691, 2224, 2586, 1694, 2713, 2992, 2205, 4055, 4778, 4726, 4700, 7142, 6655, 6785, 7270, 7949, 8169, 8742, 10218, 8874, 11375, 15885, 14264, 16933, 17925, 20622, 17529, 20599, 21695, 18830, 21992, 24273

Offset

1,3

Comments

Squares in this sequence include a(1) = 0, a(2) = 1, a(5) = 16 and a(11) = 144. Are there any others?

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

A000330(4) = 1^2 + 2^2 + 3^2 + 4^2 = 30 so a(4) = (30 mod 1^2) + (30 mod 2^2) + (30 mod 3^2) + (30 mod 4^2) = 19.

Maple

f:= proc(n) local M, k;
  M:= n*(n+1)*(2*n+1)/6;
  add(M mod k^2, k=1..n)
end proc:
map(f, [$1..100]);

Crossrefs

Cf. A000330.

Sequence in context: A195870 A125257 A195867 * A052256 A064819 A281915

Adjacent sequences: A344708 A344709 A344710 * A344712 A344713 A344714

Keyword

nonn

Author

J. M. Bergot and Robert Israel, May 26 2021

Status

approved