cp's OEIS Frontend

A380889 Integers k such that k = Sum k/(p_i + j), where p_i are the prime factors of k (with multiplicity). Case j = 1.

%I A380889 #9 Mar 02 2025 23:48:02
%S A380889 8,81,90,100,132,1125,1250,1323,1470,1485,1650,2156,2178,2420,2898,
%T A380889 3220,6348,6612,12948,15625,18375,20625,21609,24010,24255,26950,27225,
%U A380889 30250,35574,35937,36225,39930,40250,47334,47817,53130,58564,71415,74385,77924,79350
%N A380889 Integers k such that k = Sum k/(p_i + j), where p_i are the prime factors of k (with multiplicity). Case j = 1.
%C A380889 Are there other squarefree integers besides 53130?
%e A380889 53130 = 2*3*5*7*11*23 = 53130/(2+1) + 53130/(3+1) + 53130/(5+1) + 53130/(7+1) + 53130/(11+1) + 53130/(23+1);
%e A380889 124722 = 2*3^2*13^2*41 = 124722/(2+1) + 124722*2/(3+1) + 124722*2/(13+1) + 124722/(41+1).
%p A380889 with(numtheory): P:=proc(q,h) local k,n,v; v:=[];
%p A380889 for n from 1 to q do if n=add(n*k[2]/(k[1]+h),k=ifactors(n)[2]) then v:=[op(v),n]; fi;
%p A380889 od; op(v); end: P(79350,1);
%Y A380889 Cf. A380888, A380900, A380901, A380923-A380928.
%K A380889 nonn,easy
%O A380889 1,1
%A A380889 _Paolo P. Lava_, Feb 07 2025