A275660 Numbers n such that sigma(n) = Sum_{j=1..k} d(n^j) for some k, where sigma(n) is the sum of the divisors of n and d(n) is the number of divisors of n.

1, 13, 19, 34, 43, 53, 58, 89, 103, 151, 229, 251, 254, 329, 341, 349, 404, 433, 463, 593, 674, 701, 739, 859, 1033, 1223, 1429, 1483, 1506, 1670, 1709, 1826, 1846, 1886, 1889, 1948, 1951, 2067, 2091, 2143, 2255, 2308, 2431, 2699, 3001, 3079, 3319, 3739, 4003, 4093

Offset: 1

Author

Paolo P. Lava, Aug 04 2016

Keywords

• nonn

Comments

The primes in this sequence are A124199. - Robert Israel, Feb 20 2024

Examples

			d(53^1) + d(53^2) + d(53^3) + d(53^4) + d(53^5) + d(53^6) + d(53^7) + d(53^8) + d(53^9) = 54 = sigma(53).
		

Links

• Robert Israel, Table of n, a(n) for n = 1..2000

Crossrefs

Cf. A000005, A000203, A124199, A270389, A275661.

Programs

Maple

P:= proc(q) local a,k,n;
for n from 1 to q do a:=sigma(n); k:=0;
while a>0 do k:=k+1; a:=a-tau(n^k); od;
if a=0 then print(n); fi; od; end: P(10^9);