A119790 a(n) is the sum of the positive integers each of which is <= n and is divisible by exactly one prime dividing n (but is coprime to every other prime dividing n). (a(1) = 1).

1, 2, 3, 6, 5, 9, 7, 20, 18, 25, 11, 36, 13, 49, 45, 72, 17, 81, 19, 100, 84, 121, 23, 144, 75, 169, 135, 196, 29, 210, 31, 272, 198, 289, 175, 324, 37, 361, 273, 400, 41, 420, 43, 484, 405, 529, 47, 576, 196, 625, 459, 676, 53, 729, 385, 784, 570, 841, 59, 840, 61, 961

Offset: 1

Author

Leroy Quet, Jul 30 2006

Keywords

• nonn

Comments

a(n) is divisible by A026741(n). - Robert Israel, Oct 01 2017

Examples

			12 is divisible by 2 and 3. The positive integers which are <= 12 and which are divisible by 2 or 3 but not by both 2 and 3 are: 2, 3, 4, 8, 9, 10. a(12) = the sum of these integers, which is 36.
		

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A026741, A116512, A119794, A120499.

Programs

Maple

f:= proc(n) local P;
  P:= convert(numtheory:-factorset(n),list);
  convert(select(k -> nops(select(p->k mod p = 0, P))=1, [$2..n]),`+`)
end proc:
1, seq(f(n),n=2..100); # Robert Israel, Oct 01 2017

Mathematica

Table[Total@ Select[Range@ n, Function[k, Total@ Boole@ Map[Divisible[k, #] &, FactorInteger[n][[All, 1]]] == 1]], {n, 62}] (* Michael De Vlieger, Oct 01 2017 *)

Extensions

Corrected and extended by Joshua Zucker, Aug 12 2006