A132999 Imperfect numbers: Not equal to sum of proper divisors.

1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69

Offset

1,2

Comments

Imperfect numbers are either deficient numbers or abundant numbers.

References

C. A. Pickover, El prodigio de los numeros, RBA Coleccionables, 2007, p. 190.

Links

Ivan Panchenko, Table of n, a(n) for n = 1..10000

Omar E. Pol, Determinacion geometrica de los numeros primos y perfectos.

Formula

a(n) ~ n. - Charles R Greathouse IV, Feb 06 2015

Maple

with(numtheory): A132999:=n->`if`(sigma(n)=2*n, NULL, n): seq(A132999(n), n=1..100); # Wesley Ivan Hurt, Sep 11 2015

Prog

(PARI) is(n)=sigma(n, -1)!=2 \\ Charles R Greathouse IV, Feb 06 2015
(Magma) [n: n in [1..120] | not SumOfDivisors(n) eq 2*n]; // Vincenzo Librandi, Sep 12 2015

Crossrefs

Cf. A000396 (perfect numbers), A005100 (deficient numbers), A005101 (abundant numbers).

Sequence in context: A129487 A097010 A351227 * A054027 A272978 A080907

Adjacent sequences: A132996 A132997 A132998 * A133000 A133001 A133002

Keyword

easy,nonn

Author

Omar E. Pol, Oct 13 2007

Status

approved