A191580 Numbers n for which the sum of their prime factors (with repetition) divides the sum of their anti-divisors.

5, 10, 40, 41, 129, 135, 140, 155, 182, 189, 200, 204, 206, 238, 375, 429, 435, 441, 455, 475, 546, 564, 574, 616, 625, 678, 722, 744, 765, 836, 856, 902, 1035, 1056, 1170, 1188, 1272, 1296, 1344, 1518, 1650, 1764, 1806, 1918, 1925

Offset: 1

Author

Paolo P. Lava, Jun 07 2011

Keywords

• nonn
• easy

Examples

			40-> sum prime factors=2+2+2+5=11; sum anti-divisors=3+9+16+27=55; 55/11=5
129-> sum prime factors=3+43=46; sum anti-divisors=2+6+7+37+86=138; 138/46=3
		

Links

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

Crossrefs

Cf. A001414, A066272, A161917, A191581.

Programs

Maple

with(numtheory); P:=proc(i) local a,b,j,k,s,n;
for n from 3 to i do b:=ifactors(n)[2];
s:=add(b[k][1]*b[k][2],k=1..nops(b));
k:=0; j:=n; while j mod 2<>1 do k:=k+1; j:=j/2; od; a:=sigma(2*n+1)+sigma(2*n-1)+sigma(n/2^k)*2^(k+1)-6*n-2;
if type(a/s,integer) then print(n); fi; od; end: P(2000);