A322541 - OEIS

%I #8 Dec 18 2018 11:29:33

%S 114,366,1140,3660,3864,5016,11040,15210,16104,16536,18480,44772,

%T 57960,67158,68640,68880,142290,142310,155760,196248,198990,240312,

%U 248040,275520,278160,308220,322080,326424,339822,348840,352632,366792,462330,485760,607920

%N Lesser of semi-unitary amicable numbers pair: numbers (m, n) such that susigma(m) = susigma(n) = m + n, where susigma(n) is the sum of the semi-unitary divisors of n (A322485).

%e 114 is in the sequence since it is the lesser of the amicable pair (114, 126): susigma(114) = susigma(126) = 114 + 126.

%t f[p_, e_] := (p^Floor[(e + 1)/2] - 1)/(p - 1) + p^e; s[n_] := If[n == 1, 1, Times @@ (f @@@ FactorInteger[n])] - n; seq = {}; Do[n = s[m]; If[n > m && s[n] == m, AppendTo[seq, m]], {m, 1, 1000000}]; seq

%o (PARI) susigma(n) = {my(f = factor(n)); for (k=1, #f~, my(p=f[k, 1], e=f[k, 2]); f[k, 1] = (p^((e+1)\2) - 1)/(p-1) + p^e; f[k, 2] = 1; ); factorback(f); } \\ A322485

%o isok(n) = my(m=susigma(n)-n); (m > n) && (susigma(m) == n + m); \\ _Michel Marcus_, Dec 15 2018

%Y Cf. A002025, A002952, A322485, A322486, A322542.

%K nonn

%O 1,1

%A _Amiram Eldar_, Dec 14 2018