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

1, 3, 4, 6, 7, 8, 12, 12, 14, 18, 18, 20, 13, 15, 24, 30, 24, 24, 32, 36, 38, 42, 28, 44, 31, 42, 48, 32, 54, 54, 60, 42, 48, 62, 60, 68, 72, 39, 48, 74, 31, 80, 56, 72, 84, 72, 90, 72, 90, 56, 98, 102, 72, 104, 108, 96, 110, 80, 84, 84, 57, 114, 40, 114, 126, 128, 108, 60, 132, 138, 132, 96, 96, 93, 140, 150, 98, 120, 152, 144, 120, 158, 96, 164, 133, 126

Offset: 1

Author

Antti Karttunen, Apr 26 2017

Keywords

• nonn

Links

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

Crossrefs

Cf. A000203, A064216, A099774, A151799, A285702, A285704, A285705.

Programs

Mathematica

Table[DivisorSigma[1, #] &@ If[n == 1, 1, Apply[Times, FactorInteger[2 n - 1] /. {p_, e_} /; p > 2 :> NextPrime[p, -1]^e]], {n, 86}] (* Michael De Vlieger, Apr 26 2017 *)

Scheme

(define (A285703 n) (A000203 (A064216 n)))

Formula

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

Sum_{k=1..n} a(k) ~ c * n^2, where c = Product_{p prime} (p^3/((p+1)*(p^2-q(p)))) = 0.8168476756..., where q(p) = prevprime(p) (A151799) if p > 2 and q(2) = 1. - Amiram Eldar, Dec 21 2023