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

Author

Yasutoshi Kohmoto

Keywords

• nonn

Examples

			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.
		

Links

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

Crossrefs

Cf. A000203, A034448, A045796, A061765.

Programs

Mathematica

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

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

Extensions

Corrected and extended by Jud McCranie, Oct 28 2001

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