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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).

%I A119790 #24 Oct 03 2017 02:18:44
%S A119790 1,2,3,6,5,9,7,20,18,25,11,36,13,49,45,72,17,81,19,100,84,121,23,144,
%T A119790 75,169,135,196,29,210,31,272,198,289,175,324,37,361,273,400,41,420,
%U A119790 43,484,405,529,47,576,196,625,459,676,53,729,385,784,570,841,59,840,61,961
%N 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).
%C A119790 a(n) is divisible by A026741(n). - _Robert Israel_, Oct 01 2017
%H A119790 Michael De Vlieger, <a href="/A119790/b119790.txt">Table of n, a(n) for n = 1..10000</a>
%e A119790 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.
%p A119790 f:= proc(n) local P;
%p A119790   P:= convert(numtheory:-factorset(n),list);
%p A119790   convert(select(k -> nops(select(p->k mod p = 0, P))=1, [$2..n]),`+`)
%p A119790 end proc:
%p A119790 1, seq(f(n),n=2..100); # _Robert Israel_, Oct 01 2017
%t A119790 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 *)
%Y A119790 Cf. A026741, A116512, A119794, A120499.
%K A119790 nonn
%O A119790 1,2
%A A119790 _Leroy Quet_, Jul 30 2006
%E A119790 Corrected and extended by _Joshua Zucker_, Aug 12 2006