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Nontrivial nonunitary multiply perfect numbers: the sum of the nonunitary divisors of n is a positive multiple of n; i.e., (sigma(n) - usigma(n))/n is a positive integer.
7

%I #8 Jul 30 2017 22:42:13

%S 24,112,1984,2520,31320,32512,1163160,2208384,3053232,6535296,

%T 13472928,123165600,134201344,186076800,365959296,3456573120,

%U 4401782352,5517818880,18924364800,34359476224,325377803520

%N Nontrivial nonunitary multiply perfect numbers: the sum of the nonunitary divisors of n is a positive multiple of n; i.e., (sigma(n) - usigma(n))/n is a positive integer.

%t nusigma[ n_ ] := DivisorSigma[ 1, n ]-Times@@(1+Power@@#&/@FactorInteger[ n ]); For[ n=1, True, n++, v=nusigma[ n ]; If[ v>0&&Mod[ v, n ]==0, Print[ n ] ] ]

%Y Cf. A048146, A064591, A064592, A064593, A064594, A064596.

%K nonn,hard

%O 1,1

%A _Dean Hickerson_, Sep 25 2001