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A070801 Largest prime <= sigma(n): a(n) = prevprime(sigma(n)), where prevprime(n) = A007917(n), the largest prime less than or equal to n. 10
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 (list; graph; refs; listen; history; text; internal format)
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
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
Sequence in context: A245550 A318461 A085379 * A114753 A079316 A106481
KEYWORD
easy,nonn
AUTHOR
Labos Elemer, May 08 2002
STATUS
approved

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Last modified March 29 08:13 EDT 2024. Contains 371265 sequences. (Running on oeis4.)