A070801 - OEIS

%I #24 Mar 01 2024 08:46:59

%S 3,3,7,5,11,7,13,13,17,11,23,13,23,23,31,17,37,19,41,31,31,23,59,31,

%T 41,37,53,29,71,31,61,47,53,47,89,37,59,53,89,41,89,43,83,73,71,47,

%U 113,53,89,71,97,53,113,71,113,79,89,59,167,61,89,103,127,83,139,67,113,89

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

%C 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.

%H Antti Karttunen, <a href="/A070801/b070801.txt">Table of n, a(n) for n = 2..16385</a>

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

%F From _Reinhard Zumkeller_, Jun 26 2003: (Start)

%F A085379(n) <= a(n).

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

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

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

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

%t Table[Prime[PrimePi[DivisorSigma[1, w]]], {w, 2, 128}]

%t Table[NextPrime[DivisorSigma[1, n] + 1, -1], {n, 2, 128}] (* _Amiram Eldar_, Mar 01 2024 *)

%o (PARI) A070801(n) = precprime(sigma(n)); \\ _Antti Karttunen_, Nov 07 2017

%o (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

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

%K easy,nonn

%O 2,1

%A _Labos Elemer_, May 08 2002