A285704 a(n) = A285703(n) - n = A000203(A064216(n)) - n.

0, 1, 1, 2, 2, 2, 5, 4, 5, 8, 7, 8, 0, 1, 9, 14, 7, 6, 13, 16, 17, 20, 5, 20, 6, 16, 21, 4, 25, 24, 29, 10, 15, 28, 25, 32, 35, 1, 9, 34, -10, 38, 13, 28, 39, 26, 43, 24, 41, 6, 47, 50, 19, 50, 53, 40, 53, 22, 25, 24, -4, 52, -23, 50, 61, 62, 41, -8, 63, 68, 61, 24, 23, 19, 65, 74, 21, 42, 73, 64, 39, 76, 13, 80, 48, 40, 81, -10, 73, 84, 89, 88, 35, 18, -5

Offset

1,4

Links

Antti Karttunen, Table of n, a(n) for n = 1..10000

Formula

a(n) = A285703(n) - n = A000203(A064216(n)) - n.

Sum_{k=1..n} a(k) ~ c * n^2, where c = -1/2 + Product_{p prime} (p^3/((p+1)*(p^2-q(p)))) = 0.3168476756..., where q(p) = prevprime(p) (A151799) if p > 2 and q(2) = 1. - Amiram Eldar, Dec 21 2023

Mathematica

Table[-n + DivisorSigma[1, #] &@ If[n == 1, 1, Apply[Times, FactorInteger[2 n - 1] /. {p_, e_} /; p > 2 :> NextPrime[p, -1]^e]], {n, 95}] (* Michael De Vlieger, Apr 26 2017 *)

Prog

(Scheme) (define (A285704 n) (- (A285703 n) n))

Crossrefs

Cf. A000203, A001065, A064216, A151799, A285703, A285705.

Sequence in context: A134634 A346500 A103286 * A058704 A316660 A098101

Adjacent sequences: A285701 A285702 A285703 * A285705 A285706 A285707

Keyword

sign

Author

Antti Karttunen, Apr 26 2017

Status

approved