A380888 Integers k such that k = Sum k/(p_i + j), where p_i are the prime factors of k (with multiplicity). Case j = -1.

2, 9, 75, 625, 1029, 1365, 8575, 11375, 24843, 32955, 73815, 117649, 156065, 207025, 274625, 483153, 599781, 615125, 866481, 1008273, 1252815, 1337505, 1343433, 1553937, 1782105, 1955085, 2061345, 2840383, 3051015, 3432165, 3737085, 3767855, 4026275, 4998175

Offset: 1

Author

Paolo P. Lava, Feb 07 2025

Keywords

• nonn

Comments

2 is the only even term. - Chai Wah Wu, Apr 24 2025

Examples

			73815 = 3*5*7*19*37 = 73815/(3-1) + 73815/(5-1) + 73815/(7-1) + 73815/(19-1) + 73815/(37-1);
599781 = 3*7*13^4 = 599781/(3-1) + 599781/(7-1) + 599781*4/(13-1).
		

Links

• Robert Israel, Table of n, a(n) for n = 1..213

Crossrefs

Cf. A380889, A380900, A380901, A380923-A380928.

Contains A036878.

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(4998175,-1);