A105086 Sum of the divisors of n minus the least nontrivial proper divisor of n.

1, 1, 5, 1, 10, 1, 13, 10, 16, 1, 26, 1, 22, 21, 29, 1, 37, 1, 40, 29, 34, 1, 58, 26, 40, 37, 54, 1, 70, 1, 61, 45, 52, 43, 89, 1, 58, 53, 88, 1, 94, 1, 82, 75, 70, 1, 122, 50, 91, 69, 96, 1, 118, 67, 118, 77, 88, 1, 166, 1, 94, 101, 125, 79, 142, 1, 124, 93, 142, 1, 193, 1, 112

Offset: 2

Author

Toby Donaldson (tjd(AT)sfu.ca), Apr 07 2005

Keywords

• nonn

Comments

a(n) = 1 iff n is prime.

Examples

			a(6) = 10 because sigma(6) = 1 + 2 + 3 + 6 = 12, least nontrivial proper divisor(6) = 2 and their difference is 10.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 2..10000

Crossrefs

Cf. A000203, A020639.

Programs

Mathematica

a[n_] := DivisorSigma[1, n] - Divisors[n][[2]]

PARI

a(n)=sigma(n) - divisors(n)[2] \\ Charles R Greathouse IV, Dec 10 2019

Formula

a(n) = sigma(n) - least nontrivial proper divisor(n).

a(n) = A000203(n) - A020639(n), n >= 2. - Omar E. Pol, Dec 08 2019

Extensions

Edited and extended by Robert G. Wilson v, Apr 08 2005

Offset changed by Charles R Greathouse IV, Dec 10 2019