A322542 Larger 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).

126, 378, 1260, 3780, 4584, 5544, 11424, 15390, 16632, 16728, 25296, 49308, 68760, 73962, 88608, 84336, 179118, 168730, 172560, 225096, 256338, 266568, 250920, 297024, 287280, 365700, 374304, 391656, 374418, 387720, 386568, 393528, 548550, 502656, 623280

Offset

1,1

Comments

The terms are ordered according to the order of their lesser counterparts (A322541).

Links

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

Example

126 is in the sequence since it is the larger 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, n]], {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
lista(nn) = {for (n=1, nn, my(m=susigma(n)-n); if ((m > n) && (susigma(m) == n + m), print1(m, ", ")); ); } \\ Michel Marcus, Dec 15 2018

Crossrefs

Cf. A002025, A002952, A322485, A322486, A322541.

Sequence in context: A181262 A181255 A329807 * A323759 A102805 A267556

Adjacent sequences: A322539 A322540 A322541 * A322543 A322544 A322545

Keyword

nonn

Author

Amiram Eldar, Dec 14 2018

Status

approved