login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Numbers n for which the sum of their prime factors (with repetition) divides the sum of their anti-divisors.
3

%I #17 May 16 2019 08:52:51

%S 5,10,40,41,129,135,140,155,182,189,200,204,206,238,375,429,435,441,

%T 455,475,546,564,574,616,625,678,722,744,765,836,856,902,1035,1056,

%U 1170,1188,1272,1296,1344,1518,1650,1764,1806,1918,1925

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

%H Paolo P. Lava, <a href="/A191580/b191580.txt">Table of n, a(n) for n = 1..1000</a>

%e 40-> sum prime factors=2+2+2+5=11; sum anti-divisors=3+9+16+27=55; 55/11=5

%e 129-> sum prime factors=3+43=46; sum anti-divisors=2+6+7+37+86=138; 138/46=3

%p with(numtheory); P:=proc(i) local a,b,j,k,s,n;

%p for n from 3 to i do b:=ifactors(n)[2];

%p s:=add(b[k][1]*b[k][2],k=1..nops(b));

%p 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;

%p if type(a/s,integer) then print(n); fi; od; end: P(2000);

%Y Cf. A001414, A066272, A161917, A191581.

%K nonn,easy

%O 1,1

%A _Paolo P. Lava_, Jun 07 2011