A072514 Sum of n mod k for k in {1...n} with gcd(k,n) > 1.

0, 0, 0, 0, 0, 2, 0, 2, 3, 8, 0, 9, 0, 16, 17, 16, 0, 27, 0, 31, 31, 44, 0, 52, 20, 56, 36, 69, 0, 92, 0, 72, 77, 102, 68, 127, 0, 128, 97, 152, 0, 192, 0, 165, 153, 196, 0, 230, 56, 231, 170, 237, 0, 319, 154, 290, 211, 302, 0, 421, 0, 334, 273, 334, 192, 478, 0, 411, 317

Offset

1,6

Comments

Previous name was: Sum of the remainders when n is divided by unrelated numbers (numbers which are neither coprime to n nor divide n).

Links

Paolo P. Lava, Table of n, a(n) for n = 1..1000

Example

a(18) = 27: the unrelated numbers to 18 are 4, 8, 10, 12, 14, 15 and 16. The remainders when 18 is divided by these numbers are 2, 2, 8, 6, 4, 3 and 2 whose sum is 27.

Maple

seq(add(n mod k, k=select(j->gcd(j, n)>1, [$1..n])), n=1..69); # Peter Luschny, Oct 01 2014

Mathematica

snmk[n_]:=Total[Mod[n, Complement[Complement[Range[n], Divisors[n]], Select[ Range[n], CoprimeQ[ #, n]&]]]]; Array[snmk, 70] (* Harvey P. Dale, Dec 09 2018 *)

Prog

(PARI) lista(nn) = vector(nn, n, sum(i=1, n, (n % i)*(gcd(n, i) != 1))); \\ Michel Marcus, Oct 01 2014

Crossrefs

Sequence in context: A274568 A233399 A226432 * A071547 A220222 A089839

Adjacent sequences: A072511 A072512 A072513 * A072515 A072516 A072517

Keyword

nonn

Author

Amarnath Murthy, Jul 30 2002

Extensions

Corrected and extended by David Garber, Oct 22 2002

New name from Robert Israel, Oct 01 2014

Status

approved