A322486 Semi-unitary perfect numbers: numbers k such that susigma(k) = 2k, where susigma(k) is the sum of the semi-unitary divisors of k (A322485).

6, 60, 90, 264, 3960, 4560, 8736, 13770, 131040, 384384, 605880, 5765760, 20049120, 882161280, 23253135360

Offset

1,1

Comments

a(16) <= 1846273228800. - David A. Corneth, Dec 11 2018

Links

Table of n, a(n) for n=1..15.

Example

264 is in the sequence since its sum of semi-unitary divisors is susigma(264) = 528 = 2 * 264.

Mathematica

f[p_, e_] := (p^Floor[(e+1)/2] - 1)/(p-1) + p^e; susigma[n_] := If[n==1, 1, Times @@ (f @@@ FactorInteger[n])]; aQ[n_] := susigma[n]==2n; Select[Range[10000], aQ]

Prog

(PARI) ssu(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) = ssu(n) == 2*n; \\ Michel Marcus, Dec 14 2018

Crossrefs

Cf. A000396, A002827, A322485.

Sequence in context: A189000 A007358 A334406 * A323757 A331108 A324707

Adjacent sequences: A322483 A322484 A322485 * A322487 A322488 A322489

Keyword

nonn,more

Author

Amiram Eldar, Dec 11 2018

Status

approved