A325847 Lesser of exponentially-odd amicable numbers pair: numbers m < k such that m = s(k) and k = s(m), where s(k) is the sum of proper exponential-odd divisors of k.

366, 3864, 16104, 16536, 59808, 71904, 142290, 142310, 196248, 198990, 240312, 326424, 341088, 348840, 366792, 520608, 664608, 704352, 753312, 912072, 1077890, 1156870, 1184490, 1511930, 1669910, 1805490, 1863456, 1936776, 2195640, 2236570, 2517480, 2686440

Offset: 1

Author

Amiram Eldar, Sep 07 2019

Keywords

• nonn

Comments

The sum of proper exponential-odd divisors of k is A033634(k) - k if k is exponentially odd (A268335), or A033634(k) if not.

The larger counterparts are in A325848.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..789 (terms below 10^10)

Crossrefs

Cf. A033289, A033634, A268335, A325848.

Programs

Mathematica

f[e_] := If[OddQ[e], e + 2, e + 1]; fun[p_, e_] := 1 + (p^f[e] - p)/(p^2 - 1); a[1] = 1; a[n_] := Times @@ (fun @@@ (fct = FactorInteger[n])) - If[AllTrue[fct[[;; , 2]], OddQ], n, 0]; s = {}; Do[m = a[n]; If[m > n && a[m] == n, AppendTo[s, n]], {n, 1, 10^5}]; s