A064597 Nonunitary abundant numbers: the sum of the nonunitary divisors of n is larger than n; i.e., sigma(n) - usigma(n) > n.

36, 48, 72, 80, 96, 108, 120, 144, 160, 168, 180, 192, 200, 216, 224, 240, 252, 264, 280, 288, 300, 312, 320, 324, 336, 352, 360, 384, 392, 396, 400, 408, 416, 432, 448, 456, 468, 480, 504, 528, 540, 552, 560, 576, 588, 600, 612, 624, 640, 648, 672, 684

Offset: 1

Author

Dean Hickerson, Sep 25 2001

Keywords

• nonn
• easy

Examples

			The sum of the nonunitary divisors of 36 is 2 + 3 + 6 + 12 + 18 = 41.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Harry J. Smith)

Crossrefs

Cf. A048146, A063846, A064591, A064598.

Programs

Mathematica

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

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, write("b064597.txt", n++, " ", m); if (n==1000, break)) ) } \\ Harry J. Smith, Sep 19 2009