A357496 Greater of a pair of amicable numbers k < m such that s(k) = m and s(m) = k, where s(k) = A162296(k) - k is the sum of aliquot divisors of k that have a square factor.

1136, 11696, 22256, 25472, 43424, 73664, 131355, 304336, 267968, 492608, 612704, 674920, 640305, 788697, 691292, 705344, 723392, 813728, 809776, 1117395, 1258335, 1559696, 1518570, 1598368, 1821376, 2218250, 2058944, 2678752, 2744288, 2765024, 2848864, 2610656, 3134224

Offset

1,1

Comments

Analogous to amicable numbers (A002025 and A002046) with nonsquarefree divisors.

The terms are ordered according to their lesser counterparts (A357495).

Both members of each pair are necessarily nonsquarefree numbers.

Links

Amiram Eldar, Table of n, a(n) for n = 1..1000

Example

1136 is a term since s(1136) = 880 and s(880) = 1136.

Mathematica

s[n_] := Module[{f = FactorInteger[n], p, e}, p = f[[;; , 1]]; e = f[[;; , 2]]; Times @@ ((p^(e + 1) - 1)/(p - 1)) - Times @@ (p + 1) - n]; seq = {}; Do[m = s[n]; If[m > n && s[m] == n, AppendTo[seq, m]], {n, 2, 3*10^6}]; seq

Crossrefs

Cf. A162296, A325314, A322609, A357493, A357494, A357495.

Subsequence of A013929.

Similar sequences: A002046, A002953, A126166, A126170, A259039, A292981, A322542, A324709, A348344.

Sequence in context: A014365 A362543 A027545 * A113708 A353066 A206112

Adjacent sequences: A357493 A357494 A357495 * A357497 A357498 A357499

Keyword

nonn

Author

Amiram Eldar, Oct 01 2022

Status

approved