A070801 Largest prime <= sigma(n): a(n) = prevprime(sigma(n)), where prevprime(n) = A007917(n), the largest prime less than or equal to n.

3, 3, 7, 5, 11, 7, 13, 13, 17, 11, 23, 13, 23, 23, 31, 17, 37, 19, 41, 31, 31, 23, 59, 31, 41, 37, 53, 29, 71, 31, 61, 47, 53, 47, 89, 37, 59, 53, 89, 41, 89, 43, 83, 73, 71, 47, 113, 53, 89, 71, 97, 53, 113, 71, 113, 79, 89, 59, 167, 61, 89, 103, 127, 83, 139, 67, 113, 89

Offset: 2

Author

Labos Elemer, May 08 2002

Keywords

• easy
• nonn

Comments

Largest integer k such that A000203(k) <= A000203(n)+1. - Antti Karttunen, Nov 07 2017, after Benoit Cloitre's Mar 17 2002 comment in A007917.

Examples

			For n=100: sigma(100) = 217, prevprime(217) = 211 = a(100).
		

Links

• Antti Karttunen, Table of n, a(n) for n = 2..16385

Crossrefs

Cf. A000203, A007917, A070800, A000040, A000720, A023194, A085379, A085380, A085381, A202111.

Programs

Mathematica

Table[Prime[PrimePi[DivisorSigma[1, w]]], {w, 2, 128}]
Table[NextPrime[DivisorSigma[1, n] + 1, -1], {n, 2, 128}] (* Amiram Eldar, Mar 01 2024 *)

PARI

A070801(n) = precprime(sigma(n)); \\ Antti Karttunen, Nov 07 2017

Scheme

(define (A070801 n) (let ((s1 (+ 1 (A000203 n)))) (let loop ((k s1)) (if (<= (A000203 k) s1) k (loop (- k 1)))))) ;; (For code of A000203, see under that entry). Antti Karttunen, Nov 07 2017

Formula

a(n) = A000040(A000720(sigma(n))) = A007917(A000203(n)).

From Reinhard Zumkeller, Jun 26 2003: (Start)

A085379(n) <= a(n).

a(A085380(n)) = A085379(A085380(n)).

a(A085381(n)) > A085379(A085381(n)).

a(A023194(n)) = A000203(A023194(n)). (End)