A369938 Numbers whose maximal exponent in their prime factorization is a power of 2.

2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 25, 26, 28, 29, 30, 31, 33, 34, 35, 36, 37, 38, 39, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 55, 57, 58, 59, 60, 61, 62, 63, 65, 66, 67, 68, 69, 70, 71, 73, 74, 75, 76, 77

Offset

1,1

Comments

First differs from its subsequence A138302 \ {1} at n = 378: a(378) = 432 = 2^4 * 3^3 is not a term of A138302.

First differs from A096432, A220218 \ {1}, A335275 \ {1} and A337052 \ {1} at n = 56, and from A270428 \ {1} at n = 113.

Numbers k such that A051903(k) is a power of 2.

The asymptotic density of this sequence is 1/zeta(3) + Sum_{k>=2} (1/zeta(2^k+1) - 1/zeta(2^k)) = 0.87442038669659566330... .

Links

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

Mathematica

pow2Q[n_] := n == 2^IntegerExponent[n, 2];
Select[Range[2, 100], pow2Q[Max[FactorInteger[#][[;; , 2]]]] &]
Select[Range[2, 80], IntegerQ[Log2[Max[FactorInteger[#][[;; , 2]]]]]&] (* Harvey P. Dale, Nov 06 2024 *)

Prog

(PARI) ispow2(n) = n >> valuation(n, 2) == 1;
is(n) = n > 1 && ispow2(vecmax(factor(n)[, 2]));

Crossrefs

Cf. A000079, A002117, A051903.

Subsequences: A001146, A001248, A005117, A030514, A030635, A050376, A062503, A113849, A138302 \ {1}, A179645.

Similar sequences: A368714, A369937, A369939.

Cf. A096432, A220218, A270428, A335275, A337052.

Sequence in context: A377020 A220218 A096432 * A138302 A270428 A183220

Adjacent sequences: A369935 A369936 A369937 * A369939 A369940 A369941

Keyword

nonn,easy

Author

Amiram Eldar, Feb 06 2024

Status

approved