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).

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, 38, 39, 41, 42, 43, 46, 47, 51, 53, 55, 57, 58, 59, 61, 62, 65, 66, 67, 69, 70, 71, 73, 74, 77, 78, 79, 82, 83, 85, 86, 87, 89, 91, 93, 94, 95, 97, 101, 102, 103, 105, 106, 107, 109

Offset

1,2

Comments

Trivially includes all squarefree numbers (A005117). See A064595 for the others.

Links

Harry J. Smith, Table of n, a(n) for n = 1..1000

Mathematica

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

Prog

(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

Crossrefs

Cf. A048146, A064591, A064592, A064593, A064595, A064596.

Sequence in context: A064052 A248792 A358976 * A325511 A240370 A193304

Adjacent sequences: A064591 A064592 A064593 * A064595 A064596 A064597

Keyword

nonn,easy

Author

Dean Hickerson, Sep 25 2001

Status

approved