A380928 Integers k such that k = Sum k/(p_i + j), where p_i are the prime factors of k (with multiplicity). Case j = 5.

128, 6561, 6624, 250047, 252448, 253125, 264627, 267168, 290871, 293664, 342792, 377622, 381248, 557424, 648432, 762696, 841824, 1109052, 2198208, 2374464, 2472384, 5018304, 9529569, 9646875, 9765625, 10085229, 10209375, 10673289, 10775776, 11085417, 11211291

Offset: 1

Author

Paolo P. Lava, Mar 04 2025

Keywords

• nonn
• easy

Examples

			648432 = 2^4*3^3*19*79 = 648432*4/(2+5) + 648432*3/(3+5) + 648432/(19+5) + 648432/(79+5).
		

Crossrefs

Cf. A380888, A380889, A380900, A380901, A380923, A380924, A380925, A380926, A380927.

Programs

Maple

with(numtheory): P:=proc(q, h) local k, n, v; v:=[];
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; od; op(v); end: P(11211291, 5);

Mathematica

s={};j=5;f[{a_,b_}]:=Table[a,b];Do[pf=f/@FactorInteger[k]//Flatten;L=Length[pf];If[Sum[k/(pf[[i]]+j),{i,L}]==k,AppendTo[s,k]],{k,3*10^6}];s (* James C. McMahon, Mar 04 2025 *)