A064599 The sum of the nonunitary divisors of n is a divisor of n; i.e., sigma(n) - usigma(n) divides n.

4, 9, 18, 24, 25, 49, 112, 121, 169, 289, 361, 529, 841, 961, 1369, 1681, 1849, 1984, 2209, 2809, 3481, 3721, 4489, 5041, 5329, 6241, 6889, 7921, 9409, 10201, 10609, 11449, 11881, 12769, 16129, 17161, 18769, 19321, 22201, 22801, 24649, 26569

Offset: 1

Author

Dean Hickerson, Sep 25 2001

Keywords

• nonn
• easy

Comments

The sequence consists of the nonunitary perfect numbers (A064591), squares of primes (A001248) and 18.

Links

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

Crossrefs

Cf. A048146, A064591.

Programs

Mathematica

nusigma[ n_ ] := DivisorSigma[ 1, n ]-Times@@(1+Power@@#&/@FactorInteger[ n ]); For[ n=1, True, n++, v=nusigma[ n ]; If[ v>0&&Mod[ n, v ]==0, 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, v=sigma(m) - usigma(m); if (v>0 && m%v == 0, write("b064599.txt", n++, " ", m); if (n==1000, break)) ) } \\ Harry J. Smith, Sep 19 2009