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

1,2

Comments

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

Links

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

Example

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).

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);

Crossrefs

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

Sequence in context: A241120 A128342 A154076 * A088186 A089490 A057749

Adjacent sequences: A275657 A275658 A275659 * A275661 A275662 A275663

Keyword

nonn

Author

Paolo P. Lava, Aug 04 2016

Status

approved