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%I M4266 #25 Jan 29 2022 00:55:43
%S 1,6,60,90,120,36720,73440,12646368,22276800,44553600,126463680,
%T 133660800,252927360,758782080,4201148160,8402296320,28770487200,
%U 287704872000,575409744000
%N Infinitary multi-perfect numbers.
%C 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.
%D G. L. Cohen, personal communication.
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H G. L. Cohen, <a href="http://dx.doi.org/10.1090/S0025-5718-1990-0993927-5">On an integer's infinitary divisors</a>, Math. Comp., 54 (1990), 395-411.
%H Michel Marcus, <a href="/A007358/a007358.log.txt">Unexhaustive list of terms</a>
%o (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)))}
%o isok(n) = frac(a049417(n)/n) == 0; \\ _Michel Marcus_, Sep 05 2018
%Y Cf. A049417, A007357.
%Y Cf. A007691 (analog for sigma).
%K nonn,more
%O 1,2
%A _N. J. A. Sloane_
%E a(10)-a(18) from _Donovan Johnson_, Nov 21 2013
%E a(1)=1 prepended by _Michel Marcus_, Sep 04 2018
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