A371920 Abundant numbers whose abundance is also an abundant number.

24, 30, 42, 54, 60, 66, 78, 84, 90, 96, 102, 112, 114, 120, 126, 132, 138, 140, 150, 156, 168, 174, 176, 180, 186, 198, 204, 208, 210, 216, 222, 224, 228, 234, 240, 246, 252, 258, 264, 270, 276, 280, 282, 294, 304, 306, 308, 312, 318, 330, 336, 342, 348, 354, 360

Offset

1,1

Comments

First differs from A125639 at n = 12.

Numbers k such that A033880(k) > 0 and A033880(A033880(k)) > 0.

This sequence is infinite: if m is divisible by 6 and coprime to 5, then 5*m is a term.

All the multiply-perfect numbers (A007691) that are not 1 or perfect (A000396), i.e., the terms of A166069, are terms of this sequence.

Links

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

Example

24 is a term since A033880(24) = 12 > 0 and A033880(12) = 4 > 0.

Mathematica

ab[n_] := DivisorSigma[1, n] - 2*n; q[n_] := Module[{k = ab[n]}, k > 0 && ab[k] > 0]; Select[Range[360], q]

Prog

(PARI) ab(n) = sigma(n) - 2*n;
is(n) = {my(k = ab(n)); k > 0 && ab(k) > 0; }

Crossrefs

Cf. A033880 (abundance), A000396, A007691, A125639.

Subsequence of A005101.

Subsequences: A141545, A166069, A223610, A223611, A223613.

Sequence in context: A335054 A348604 A347063 * A125639 A125640 A141545

Adjacent sequences: A371917 A371918 A371919 * A371921 A371922 A371923

Keyword

nonn,easy

Author

Amiram Eldar, Apr 12 2024

Status

approved