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%I #10 Jul 30 2017 22:42:55
%S 1,2,3,5,6,7,10,11,13,14,15,17,19,21,22,23,24,26,29,30,31,33,34,35,37,
%T 38,39,41,42,43,46,47,51,53,55,57,58,59,61,62,65,66,67,69,70,71,73,74,
%U 77,78,79,82,83,85,86,87,89,91,93,94,95,97,101,102,103,105,106,107,109
%N Nonunitary multiply perfect numbers: the sum of the nonunitary divisors of n is a multiple of n; i.e., n divides sigma(n) - usigma(n).
%C Trivially includes all squarefree numbers (A005117). See A064595 for the others.
%H Harry J. Smith, <a href="/A064594/b064594.txt">Table of n, a(n) for n = 1..1000</a>
%t nusigma[ n_ ] := DivisorSigma[ 1, n ]-Times@@(1+Power@@#&/@FactorInteger[ n ]); For[ n=1, True, n++, If[ Mod[ nusigma[ n ], n ]==0, Print[ n ] ] ]
%o (PARI) usigma(n)= { local(f,s=1); f=factor(n); for(i=1, matsize(f)[1], s*=1 + f[i, 1]^f[i, 2]); return(s) } { n=0; for (m=1, 10^9, if ((sigma(m) - usigma(m)) % m == 0, write("b064594.txt", n++, " ", m); if (n==1000, break)) ) } \\ _Harry J. Smith_, Sep 19 2009
%Y Cf. A048146, A064591, A064592, A064593, A064595, A064596.
%K nonn,easy
%O 1,2
%A _Dean Hickerson_, Sep 25 2001
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