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

2,1

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.

Links

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

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)

Example

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

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 *)

Prog

(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

Crossrefs

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

Sequence in context: A245550 A318461 A085379 * A114753 A079316 A106481

Adjacent sequences: A070798 A070799 A070800 * A070802 A070803 A070804

Keyword

easy,nonn

Author

Labos Elemer, May 08 2002

Status

approved