A325847 - OEIS

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.

%I #35 Sep 10 2019 21:43:24

%S 366,3864,16104,16536,59808,71904,142290,142310,196248,198990,240312,

%T 326424,341088,348840,366792,520608,664608,704352,753312,912072,

%U 1077890,1156870,1184490,1511930,1669910,1805490,1863456,1936776,2195640,2236570,2517480,2686440

%N 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.

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

%C The larger counterparts are in A325848.

%H Amiram Eldar, <a href="/A325847/b325847.txt">Table of n, a(n) for n = 1..789</a> (terms below 10^10)

%t 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

%Y Cf. A033289, A033634, A268335, A325848.

%K nonn

%O 1,1

%A _Amiram Eldar_, Sep 07 2019