A380846 Numbers k such that A380845(k) = 2*k.

18, 42, 90, 186, 196, 306, 378, 420, 534, 618, 654, 690, 762, 834, 868, 906, 1062, 1110, 1194, 1242, 1326, 1362, 1422, 1458, 1530, 1698, 1764, 1818, 1866, 2118, 2214, 2262, 2324, 2346, 2490, 2598, 2670, 2706, 2730, 2778, 2838, 2862, 2884, 2922, 2958, 2994, 3066, 3138

Offset: 1

Author

Amiram Eldar, Feb 05 2025

Keywords

• nonn
• base
• easy

Comments

Analogous to perfect numbers (A000396) with A380845 instead of A000203.

All the terms are abundant numbers (A005101), since A380845(k) <= A000203(k) with equality only when k is a power of 2, and powers of 2 are deficient numbers (A005100).

Are there odd terms in this sequence? There are none below 10^11.

Examples

			18 is a term since A380845(18) = 36 = 2 * 18.
		

Links

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

Crossrefs

Cf. A000203, A000396, A005100, A380845, A380847, A380848.

Subsequence of A005101.

Programs

Mathematica

q[k_] := Module[{h = DigitCount[k, 2, 1]}, DivisorSum[k, # &, DigitCount[#, 2, 1] == h &] == 2*k]; Select[Range[3200], q]

PARI

isok(k) = {my(h = hammingweight(k)); sumdiv(k, d, d*(hammingweight(d) == h)) == 2*k;}