A045795 Unitary-sigma sigma multiply perfect numbers: numbers k such that A061765(k) = m*k for some integer m.

1, 2, 4, 8, 10, 16, 24, 27, 30, 54, 63, 64, 108, 126, 165, 238, 252, 360, 432, 504, 512, 660, 864, 952, 1008, 1536, 1728, 2016, 2464, 2640, 4032, 4096, 5544, 10560, 13824, 16728, 17640, 23040, 32256, 45500, 47360, 60928, 65536, 110592, 152064, 153600

Offset

1,2

Links

Donovan Johnson, Table of n, a(n) for n = 1..100

Example

Sigma(10) = 18 = 2*3^2, usigma(18) = (2+1)*(9+1) = 30, divisible by 10, so 10 is in the sequence.
Sigma(24) = 60 = 2^2*3*5, usigma(60) = 5*4*6 = 120, divisible by 24, so 24 is in the sequence.

Mathematica

q[n_] := Divisible[Times @@ (1 + Power @@@ FactorInteger[DivisorSigma[1, n]]), n]; Select[Range[200000], q] (* Amiram Eldar, Aug 26 2022 *)

Prog

(PARI) for(n=1, 10^9, s=sigma(n); om=omega(s); f=factorint(s); pr=1; for(j=1, om, pr=pr*(f[j, 1]^f[j, 2]+1)); if(pr%n==0, print(n))) \\ Donovan Johnson, Mar 12 2013

Crossrefs

Cf. A000203, A034448, A045796, A061765.

Sequence in context: A102248 A161374 A272062 * A226816 A371291 A335238

Adjacent sequences: A045792 A045793 A045794 * A045796 A045797 A045798

Keyword

nonn

Author

Yasutoshi Kohmoto

Extensions

Corrected and extended by Jud McCranie, Oct 28 2001

Missing first term added and offset corrected by Donovan Johnson, Mar 12 2013

Status

approved