A322541 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).

114, 366, 1140, 3660, 3864, 5016, 11040, 15210, 16104, 16536, 18480, 44772, 57960, 67158, 68640, 68880, 142290, 142310, 155760, 196248, 198990, 240312, 248040, 275520, 278160, 308220, 322080, 326424, 339822, 348840, 352632, 366792, 462330, 485760, 607920

Offset

1,1

Links

Table of n, a(n) for n=1..35.

Example

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

Mathematica

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

Prog

(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
isok(n) = my(m=susigma(n)-n); (m > n) && (susigma(m) == n + m); \\ Michel Marcus, Dec 15 2018

Crossrefs

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

Sequence in context: A250725 A300478 A305066 * A323758 A043403 A122279

Adjacent sequences: A322538 A322539 A322540 * A322542 A322543 A322544

Keyword

nonn

Author

Amiram Eldar, Dec 14 2018

Status

approved