A322541 - OEIS

The OEIS is supported by the many generous donors to the OEIS Foundation.

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give

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

(list; graph; refs; listen; history; text; internal format)

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