A360639 Numbers k such that k and k+2 are both A000120-perfect numbers (A175522).

123, 219, 695, 1261, 1851, 1943, 3543, 5963, 7031, 7613, 7769, 7861, 10081, 11357, 11629, 12083, 13211, 13791, 14185, 15699, 15835, 15929, 16241, 18649, 20197, 20989, 22521, 23449, 23521, 23963, 24461, 27215, 27829, 28263, 28367, 29485, 29651, 30359, 30901, 31803

Offset: 1

Author

Amiram Eldar, Feb 15 2023

Keywords

• nonn
• base

Comments

The smallest gap between two consecutive A000120-perfect numbers is 2.

All terms of this sequence are odd.

Examples

			123 is a term since 123 and 125 are both in A175522: A093653(123)/A000120(123) = A093653(125)/A000120(125) = 12/6 = 2.
		

Links

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

Crossrefs

Subsequence of A175522.

Cf. A000120, A093653, A338452, A360640.

Programs

Mathematica

q[n_] := DivisorSum[n, DigitCount[#, 2, 1] &] == 2 * DigitCount[n, 2, 1]; seq[kmax_] := Module[{s = {}, k = 1, q1 = False, q2}, Do[q2 = q[k]; If[q1 && q2, AppendTo[s, k-2]]; q1 = q2, {k, 3, kmax, 2}]; s]; seq[32000]

PARI

lista(kmax) = {my(is1 = 0, is2); forstep(k=1, kmax, 2, is2 = (sumdiv(k, d, hammingweight(d)) == 2*hammingweight(k)); if(is1 && is2, print1(k-2, ", ")); is1 = is2); }