A064599 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

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)

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 ] ] ]

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, 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

CROSSREFS

Cf. A048146, A064591.

Sequence in context: A313357 A313358 A263351 * A368780 A062952 A344405

Adjacent sequences: A064596 A064597 A064598 * A064600 A064601 A064602

KEYWORD

nonn,easy

AUTHOR

Dean Hickerson, Sep 25 2001

STATUS

approved