A380924 -id:A380924 - cp's OEIS frontend

A380923 Integers k such that k = Sum k/(p_i + j), where p_i are the prime factors of k (with multiplicity). Case j = -3.

25, 245, 1250, 2401, 4235, 12250, 41503, 62500, 73205, 120050, 136045, 138985, 211750, 215215, 612500, 717409, 1176490, 1333241, 1362053, 1856465, 2075150, 2109107, 2351635, 2402455, 3125000, 3660250, 3720145, 4561235, 5330605, 5535985, 6002500, 6802250, 6949250

Offset: 1

Paolo P. Lava, Mar 03 2025

			138985 = 5*7*11*19^2 = 138985/(5-3) +138985/(7-3) +138985/(11-3) +138985*2/(19-3)

Cf. A380888, A380889, A380900, A380901, A380924 - A380928.

with(numtheory): P:=proc(q,h) global k,n,v; v:=[];
for n from 1 to q do if n mod 3>0 then if n=add(n*k[2]/(k[1]+h),k=ifactors(n)[2]) then v:=[op(v),n];
print(n); fi; fi; od; op(v); end: P(6949250,-3);

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

Paolo P. Lava, Mar 04 2025

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

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

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);

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 *)

A380925 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

5, 75, 100, 343, 1125, 1500, 2000, 5145, 6860, 16875, 22500, 30000, 40000, 77175, 102900, 107653, 137200, 253125, 337500, 352947, 450000, 470596, 600000, 800000, 1157625, 1543500, 1614795, 2058000, 2153060, 2744000, 3796875, 5062500, 5294205, 6750000, 7058940

Offset: 1

Paolo P. Lava, Mar 03 2025

			337500 = 2^2*3^3*5^5 = 337500*2/(2-4) + 337500*3/(3-4) + 337500*5/(5-4)

Cf. A380888, A380889, A380900, A380901, A380923, A380924, A380926 - A380928.

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(7058940, -4);

cp's OEIS Frontend

A380923 Integers k such that k = Sum k/(p_i + j), where p_i are the prime factors of k (with multiplicity). Case j = -3.

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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.

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Mathematica

A380925 Integers k such that k = Sum k/(p_i + j), where p_i are the prime factors of k (with multiplicity). Case j = -4.

Views

Author

Keywords

Examples

Crossrefs

Programs

Maple