Search: id:A064594
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%I A064594
%S A064594 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 A064594 38,39,41,42,43,46,47,51,53,55,57,58,59,61,62,65,66,67,69,70,71,73,74,
%U A064594 77,78,79,82,83,85,86,87,89,91,93,94,95,97,101,102,103,105,106,107,109
%N A064594 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 A064594 Trivially includes all square-free numbers (A005117). See A064595 for 
               the others.
%H A064594 Harry J. Smith, <a href="b064594.txt">Table of n, a(n) for n=1,...,1000</
               a>
%t A064594 nusigma[ n_ ] := DivisorSigma[ 1, n ]-Times@@(1+Power@@#&/@FactorInteger[ 
               n ]); For[ n=1, True, n++, If[ Mod[ nusigma[ n ], n ]==0, Print[ 
               n ] ] ]
%o A064594 (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)) ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Sep 
               19 2009]
%Y A064594 Cf. A048146, A064591, A064592, A064593, A064595, A064596.
%Y A064594 Sequence in context: A048839 A122144 A064052 this_sequence A076144 A005117 
               A144338
%Y A064594 Adjacent sequences: A064591 A064592 A064593 this_sequence A064595 A064596 
               A064597
%K A064594 nonn,easy
%O A064594 1,2
%A A064594 Dean Hickerson (dean.hickerson(AT)yahoo.com), Sep 25, 2001

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