A120444 First differences of A004125.

0, 1, 0, 3, -1, 5, 0, 4, 1, 9, -5, 11, 3, 5, 0, 15, -4, 17, -3, 9, 7, 21, -13, 18, 9, 13, -1, 27, -13, 29, 0, 17, 13, 21, -20, 35, 15, 21, -11, 39, -13, 41, 3, 11, 19, 45, -29, 40, 6, 29, 5, 51, -13, 37, -9, 33, 25, 57, -49, 59, 27, 21, 0, 45, -13, 65, 9, 41, -5, 69, -52, 71, 33, 25, 11, 57, -13, 77, -27, 40, 37, 81, -57, 61, 39, 53, -5

Offset: 1

Author

John W. Layman, Jul 19 2006

Keywords

• sign
• easy

Comments

It appears that (1) a(n)=0 if and only if n is a power of 2 and (2) a(n)=n-1 if and only if n+1 is a prime. (This has been verified for the first 2000 terms.)

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000203, A004125, A005408.

Programs

Haskell

a120444 n = a120444_list !! (n-1)
a120444_list = zipWith (-) (tail a004125_list) a004125_list
-- Reinhard Zumkeller, May 30 2015

Mathematica

Table[2*m - 1 - DivisorSigma[1, m], {m, 2, 100}] (* Paolo Xausa, Dec 09 2024 *)

Formula

a(n) = A005408(n) - A000203(n+1). - Omar E. Pol, Jan 24 2014