

A336591


Numbers whose exponents in their prime factorization are either 1, 3, or both.


2



1, 2, 3, 5, 6, 7, 8, 10, 11, 13, 14, 15, 17, 19, 21, 22, 23, 24, 26, 27, 29, 30, 31, 33, 34, 35, 37, 38, 39, 40, 41, 42, 43, 46, 47, 51, 53, 54, 55, 56, 57, 58, 59, 61, 62, 65, 66, 67, 69, 70, 71, 73, 74, 77, 78, 79, 82, 83, 85, 86, 87, 88, 89, 91, 93, 94, 95
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,2


COMMENTS

The asymptotic density of this sequence is zeta(6)/(zeta(2) * zeta(3)) * Product_{p prime} (1 + 2/p^3  1/p^4 + 1/p^5) = 0.68428692418686231814196872579121808347231273672316377728461822629005... (Cohen, 1962).
First differs from A036537 at n = 89. A036537(89) = 128 = 2^7 is not a term of this sequence.


LINKS

Amiram Eldar, Table of n, a(n) for n = 1..10000
Eckford Cohen, Arithmetical notes. III. Certain equally distributed sets of integers, Pacific Journal of Mathematics, No. 12, Vol. 1 (1962), pp. 7784.


EXAMPLE

1 is a term since it has no exponents, and thus it has no exponent that is not 1 or 3.
2 is a term since 2 = 2^1 has only the exponent 1 in its prime factorization.
24 is a term since 24 = 2^3 * 3^1 has the exponents 1 and 3 in its prime factorization.


MATHEMATICA

seqQ[n_] := AllTrue[FactorInteger[n][[;; , 2]], MemberQ[{1, 3}, #] &]; Select[Range[100], seqQ]


CROSSREFS

Subsequence of A036537 and A268335.
A005117 and A062838 are subsequences.
Cf. A068468.
Sequence in context: A162644 A268335 A002035 * A036537 A072510 A084116
Adjacent sequences: A336588 A336589 A336590 * A336592 A336593 A336594


KEYWORD

nonn


AUTHOR

Amiram Eldar, Jul 26 2020


STATUS

approved



