A152864 Deficiency of n, plus the number of proper divisors of n: a(n) = 2n - sigma(n) + d(n) - 1.

1, 2, 3, 3, 5, 3, 7, 4, 7, 5, 11, 1, 13, 7, 9, 5, 17, 2, 19, 3, 13, 11, 23, -5, 21, 13, 17, 5, 29, -5, 31, 6, 21, 17, 25, -11, 37, 19, 25, -3, 41, -5, 43, 9, 17, 23, 47, -19, 43, 12, 33, 11, 53, -5, 41, -1, 37, 29, 59, -37, 61, 31

Offset: 1

Author

Omar E. Pol, Dec 14 2008

Keywords

• easy
• sign

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000005, A000203, A005843, A032741, A033879, A152770, A152771, A152772.

Programs

Mathematica

a[n_] := 2*n - Differences[DivisorSigma[{0, 1}, n]][[1]] - 1; Array[a, 100] (* Amiram Eldar, Apr 07 2024 *)

PARI

a(n) = 2*n - sigma(n) + numdiv(n) - 1; \\ Amiram Eldar, Apr 07 2024

Formula

a(n) = A005843(n)-A000203(n)+A000005(n)-1 = A033879(n)+A032741(n).