A362841 Numbers with at least one 5 in their prime signature.

32, 96, 160, 224, 243, 288, 352, 416, 480, 486, 544, 608, 672, 736, 800, 864, 928, 972, 992, 1056, 1120, 1184, 1215, 1248, 1312, 1376, 1440, 1504, 1568, 1632, 1696, 1701, 1760, 1824, 1888, 1944, 1952, 2016, 2080, 2144, 2208, 2272, 2336, 2400, 2430, 2464, 2528, 2592, 2656, 2673, 2720, 2784, 2848, 2912, 2976

Offset: 1

Author

R. J. Mathar, May 05 2023

Keywords

• nonn

Comments

Contains all odd multiples of 2^5: Each second term of A174312 is in this sequence.

The asymptotic density of this sequence is 1 - Product_{p prime} (1 - 1/p^5 + 1/p^6) = 0.01863624892... . - Amiram Eldar, May 05 2023

Examples

			Contains 2^5, 2^5*3, 2^5*5, 2^5*7, 3^5, 2^5*3^2, 2^5*11, 2^5*13, 2^5*3*5, 2*3^5, etc.
		

Links

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

Crossrefs

Cf. A038109 (at least one 2), A176297 (at least one 3), A050997 (subsequence), A178740 (subsequence), A179646 (subsequence), A179667 (subsequence), A179671 (subsequence), A174312.

Programs

Mathematica

Select[Range[3000], MemberQ[FactorInteger[#][[;;, 2]], 5] &] (* Amiram Eldar, May 05 2023 *)