A166982 Numbers whose number of ordered factorizations is a perfect power.

1, 2, 3, 5, 7, 8, 11, 12, 13, 16, 17, 18, 19, 20, 23, 27, 28, 29, 31, 32, 37, 41, 43, 44, 45, 47, 50, 52, 53, 59, 61, 63, 64, 67, 68, 71, 73, 75, 76, 79, 81, 83, 89, 92, 97, 98, 99, 101, 103, 107, 109, 113, 116, 117, 124, 125, 127, 128, 131, 137, 139, 147, 148, 149

Offset

1,2

Comments

Numbers k such that A074206(k) is a perfect power.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Mathematica

f[1] = 1; f[n_] := f[n] = DivisorSum[n, f[#] &, # < n &]; ppQ[n_] := n == 1 || GCD @@ FactorInteger[n][[;; , 2]] > 1; Select[Range[150], ppQ[f[#]] &] (* Amiram Eldar, May 01 2025 *)

Crossrefs

Cf. A001597, A002033, A074206.

Sequence in context: A100959 A245303 A359766 * A026422 A026424 A298207

Adjacent sequences: A166979 A166980 A166981 * A166983 A166984 A166985

Keyword

nonn

Author

Juri-Stepan Gerasimov, Oct 26 2009

Extensions

Name corrected and more terms added by Amiram Eldar, May 01 2025

Status

approved