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.
Original entry on oeis.org
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
648432 = 2^4*3^3*19*79 = 648432*4/(2+5) + 648432*3/(3+5) + 648432/(19+5) + 648432/(79+5).
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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);
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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 *)
A380924
Integers k such that k = Sum k/(p_i + j), where p_i are the prime factors of k (with multiplicity). Case j = 3.
Original entry on oeis.org
32, 729, 756, 784, 16875, 17500, 18522, 19208, 22950, 23800, 31212, 32368, 37000, 50320, 243760, 390625, 428750, 453789, 470596, 531250, 562275, 570375, 583100, 591500, 722500, 764694, 775710, 793016, 804440, 874125, 906500, 982600, 1188810, 1232840, 1250600
Offset: 1
562275 = 3^3*5^2*7^2*17 = 562275*3/(3+3) + 562275*2/(5+3) + 562275*2/(7+3) + 562275/(17+3)
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with(numtheory): P:=proc(q, h) local k, n, v; v:=[];
for n from 1 by 2 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(1250600, 3);
A380926
Integers k such that k = Sum k/(p_i + j), where p_i are the prime factors of k (with multiplicity). Case j = 4.
Original entry on oeis.org
64, 2000, 2187, 2448, 62500, 76500, 93636, 110484, 159300, 514836, 1953125, 2390625, 2576816, 2926125, 3452625, 3581577, 4009008, 4226013, 4365680, 4615408, 4730352, 4866800, 4978125, 5581488, 6084477, 6093225, 6810608, 6820400, 7396400, 8047600, 8909109, 9456240
Offset: 1
514836 = 2^2*3^4*7*227 = 514836*2/(2+4) + 514836*4/(3+4) + 514836/(7+4) + 514836/(227+4)
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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(9456240, 4);
Showing 1-3 of 3 results.