A007358 Infinitary multi-perfect numbers.

1, 6, 60, 90, 120, 36720, 73440, 12646368, 22276800, 44553600, 126463680, 133660800, 252927360, 758782080, 4201148160, 8402296320, 28770487200, 287704872000, 575409744000

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• more

Comments

The sequence contains numbers n such that A049417(n) = k*n for some integer k>=1. A007357 is the subsequence with quotient k=2. Cohen lists n=120, 73440, 44553600, 252927360, 575409744000 as entries with k=3, provides seven entries with k=4 and two entries with k=5.

References

• G. L. Cohen, personal communication.
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• G. L. Cohen, On an integer's infinitary divisors, Math. Comp., 54 (1990), 395-411.
• Michel Marcus, Unexhaustive list of terms

Crossrefs

Cf. A049417, A007357.

Cf. A007691 (analog for sigma).

Programs

PARI

a049417(n) = {my(b, f=factorint(n)); prod(k=1, #f[, 2], b = binary(f[k, 2]); prod(j=1, #b, if(b[j], 1+f[k, 1]^(2^(#b-j)), 1)))}
isok(n) = frac(a049417(n)/n) == 0; \\ Michel Marcus, Sep 05 2018

Extensions

a(10)-a(18) from Donovan Johnson, Nov 21 2013

a(1)=1 prepended by Michel Marcus, Sep 04 2018