Amiram Eldar, <a href="/A369938/b369938_1.txt">Table of n, a(n) for n = 1..10000</a>

reviewed

approved

OEIS Server: Installed first b-file as b369938.txt.

proposed

reviewed

editing

proposed

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

Amiram Eldar, <a href="/A369938/b369938_1.txt">Table of n, a(n) for n = 1..10000</a>

allocatedNumbers whose maximal exponent in their prime factorization is a forpower Amiramof Eldar2.

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

1,1

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, 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... .

pow2Q[n_] := n == 2^IntegerExponent[n, 2];

Select[Range[2, 100], pow2Q[Max[FactorInteger[#][[;; , 2]]]] &]

(PARI) ispow2(n) = n >> valuation(n, 2) == 1;

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

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.

allocated

nonn,easy

Amiram Eldar, Feb 06 2024

approved

editing

allocated for Amiram Eldar

allocated

approved