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

1,1

Comments

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

All terms of this sequence are odd.

Links

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

Example

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

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]

Prog

(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); }

Crossrefs

Subsequence of A175522.

Cf. A000120, A093653, A338452, A360640.

Sequence in context: A302459 A179127 A153254 * A227522 A193431 A306643

Adjacent sequences: A360636 A360637 A360638 * A360640 A360641 A360642

Keyword

nonn,base

Author

Amiram Eldar, Feb 15 2023

Status

approved