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

Author

Amiram Eldar, Apr 12 2024

Keywords

• nonn
• easy

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.

Examples

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

Links

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

Crossrefs

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

Subsequence of A005101.

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

Programs

Mathematica

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

PARI

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