A357495 Lesser 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.

880, 10480, 20080, 24928, 42976, 69184, 110565, 252080, 267712, 489472, 566656, 569240, 603855, 626535, 631708, 687424, 705088, 741472, 786896, 904365, 1100385, 1234480, 1280790, 1425632, 1749824, 1993750, 2012224, 2401568, 2439712, 2496736, 2542496, 2573344, 2671856

Offset

1,1

Comments

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

The larger counterparts are in A357496.

Both members of each pair are necessarily nonsquarefree numbers.

Links

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

Example

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

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, n]], {n, 2, 3*10^6}]; seq

Crossrefs

Cf. A162296, A325314, A322609, A357493, A357494, A357496.

Subsequence of A013929.

Similar sequences: A002025, A002952, A126165, A126169, A259038, A292980, A322541, A324708, A348343.

Sequence in context: A118799 A050424 A206341 * A024393 A006052 A105976

Adjacent sequences: A357492 A357493 A357494 * A357496 A357497 A357498

Keyword

nonn

Author

Amiram Eldar, Oct 01 2022

Status

approved