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A366762
Numbers whose canonical prime factorization contains only exponents which are congruent to 1 modulo 3.
5
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 A274034 at n = 42, and from A197680 and A361177 at n = 84.
The asymptotic density of this sequence is zeta(3) * Product_{p prime} (1 - 1/p^2 - 1/p^3 + 1/p^4) = A002117 * A330523 = A253905 * A065465 = 0.644177671086029533405... .
LINKS
FORMULA
Sum_{n>=1} 1/a(n)^s = zeta(3*s) * Product_{p prime} (1 + 1/p^s - 1/p^(3*s)), for s > 1.
MATHEMATICA
q[n_] := AllTrue[FactorInteger[n][[;; , 2]], Mod[#, 3] == 1 &]; Select[Range[120], q]
PROG
(PARI) is(n) = {my(f = factor(n)); for(i = 1, #f~, if(f[i, 2]%3 != 1, return(0))); 1; }
CROSSREFS
Similar sequences with exponents of a given form: A000290 (2*k), A268335 (2*k+1), A000578 (3*k), A182120 (3*k+2).
Sequence in context: A274034 A197680 A361177 * A369210 A369937 A119024
KEYWORD
nonn,easy
AUTHOR
Amiram Eldar, Oct 21 2023
STATUS
approved