A380847 Numbers k such that A380845(k) = 3*k.

1800, 3720, 7560, 15240, 20832, 30600, 42336, 61320, 85344, 109320, 116040, 122760, 171360, 218760, 238920, 245640, 343392, 346440, 395880, 437640, 462600, 484680, 491400, 580680, 687456, 854760, 875400, 896520, 917880, 925320, 950520, 954120, 976200, 982920, 1011720

Offset: 1

Author

Amiram Eldar, Feb 05 2025

Keywords

• nonn
• base
• easy

Comments

Analogous to triperfect numbers (A005820) with A380845 instead of A000203.

All the terms are 3-abundant numbers (A068403), because A380845(k) <= A000203(k) with equality only when k is a power of 2, and powers of 2 are deficient numbers (A005100).

Examples

			1800 is a term since A380845(18) = 5400 = 3 * 1800.
		

Links

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

Crossrefs

Cf. A000203, A005100, A005820, A380845, A380846, A380848.

Subsequence of A068403.

Programs

Mathematica

q[k_] := Module[{h = DigitCount[k, 2, 1]}, DivisorSum[k, # &, DigitCount[#, 2, 1] == h &] == 3*k]; Select[Range[10^6], q]

PARI

isok(k) = {my(h = hammingweight(k)); sumdiv(k, d, d*(hammingweight(d) == h)) == 3*k;}