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

Author

Omar E. Pol, Oct 13 2007

Keywords

• easy
• nonn

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.

Crossrefs

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

Programs

Magma

[n: n in [1..120] | not SumOfDivisors(n) eq 2*n]; // Vincenzo Librandi, Sep 12 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

PARI

is(n)=sigma(n,-1)!=2 \\ Charles R Greathouse IV, Feb 06 2015

Formula

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