A361177 Exponentially powerful numbers: numbers whose exponents in their canonical prime factorization are all powerful numbers (A001694).

1, 2, 3, 5, 6, 7, 10, 11, 13, 14, 15, 16, 17, 19, 21, 22, 23, 26, 29, 30, 31, 33, 34, 35, 37, 38, 39, 41, 42, 43, 46, 47, 48, 51, 53, 55, 57, 58, 59, 61, 62, 65, 66, 67, 69, 70, 71, 73, 74, 77, 78, 79, 80, 81, 82, 83, 85, 86, 87, 89, 91, 93, 94, 95, 97, 101, 102

Offset

1,2

Comments

First differs from it subsequence A197680 at n = 167: a(167) = 256 is not a term of A197680.

The asymptotic density of this sequence is Product_{p prime} ((1 - 1/p)*(1 + Sum_{i>=1} 1/p^A001694(i))) = 0.6427901996... .

Links

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

Mathematica

powQ[n_] := n == 1 || Min[FactorInteger[n][[;; , 2]]] > 1; Select[Range[100], AllTrue[FactorInteger[#][[;; , 2]], powQ] &]

Prog

(PARI) ispow(n) = {n == 1 || vecmin(factor(n)[, 2]) > 1; }
is(n) = {my(e = factor(n)[, 2]); if(n == 1, return(1)); for(i=1, #e, if(!ispow(e[i]), return(0))); 1; }

Crossrefs

Cf. A001694.

Similar sequences: A197680, A209061, A138302, A268335.

Sequence in context: A336224 A274034 A197680 * A366762 A369210 A369937

Adjacent sequences: A361174 A361175 A361176 * A361178 A361179 A361180

Keyword

nonn

Author

Amiram Eldar, Mar 03 2023

Status

approved