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A361177
Exponentially powerful numbers: numbers whose exponents in their canonical prime factorization are all powerful numbers (A001694).
6
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
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
KEYWORD
nonn
AUTHOR
Amiram Eldar, Mar 03 2023
STATUS
approved