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.

8, 81, 90, 100, 132, 1125, 1250, 1323, 1470, 1485, 1650, 2156, 2178, 2420, 2898, 3220, 6348, 6612, 12948, 15625, 18375, 20625, 21609, 24010, 24255, 26950, 27225, 30250, 35574, 35937, 36225, 39930, 40250, 47334, 47817, 53130, 58564, 71415, 74385, 77924, 79350

Offset: 1

Author

Paolo P. Lava, Feb 07 2025

Keywords

• nonn
• easy

Comments

Are there other squarefree integers besides 53130?

Examples

			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);
124722 = 2*3^2*13^2*41 = 124722/(2+1) + 124722*2/(3+1) + 124722*2/(13+1) + 124722/(41+1).
		

Crossrefs

Cf. A380888, A380900, A380901, A380923-A380928.

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(79350,1);