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A181468 Numbers n such that 83 is the largest prime factor of n^2-1. 3
82, 84, 165, 167, 248, 331, 414, 497, 499, 582, 665, 829, 831, 914, 995, 1080, 1161, 1246, 1327, 1329, 1495, 1576, 1825, 1910, 2076, 2157, 2159, 2323, 2406, 2408, 2738, 2821, 2906, 2989, 3070, 3238, 3319, 3485, 3568, 3651, 3653, 3817, 4149, 4234, 4481 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Sequence is finite, for proof see A175607.

Search for terms can be restricted to the range from 2 to A175607(23) = 34903240221563713; primepi(83) = 23.

LINKS

A. Jasinski, Table of n, a(n) for n = 1..2082

MATHEMATICA

jj = 2^36*3^23*5^15*7^13*11^10*13^9*17^8*19^8*23^8*29^7*31^7*37^7*41^6 *43^6*47^6*53^6*59^6*61^6*67^6*71^5*73^5*79^5*83^5*89^5*97^5; rr = {}; n = 2; While[n < 3222617400, If[GCD[jj, n^2 - 1] == n^2 - 1, k = FactorInteger[n^2 - 1]; kk = Last[k][[1]]; If[kk == 83, AppendTo[rr, n]]]; n++ ]; rr (* Artur Jasinski *)

Select[Range[300000], FactorInteger[#^2-1][[-1, 1]]==83&]

PROG

(MAGMA) [ n: n in [2..300000] | m eq 83 where m is D[#D] where D is PrimeDivisors(n^2-1) ]; // Klaus Brockhaus, Feb 21 2011

(MAGMA) p:=(97*89*83*79*73*71)^5 *(67*61*59*53*47*43*41)^6 *(37*31*29)^7 *(23*19*17)^8 *13^9 *11^10 *7^13 *5^15 *3^23 *2^36; [ n: n in [2..50000000] | p mod (n^2-1) eq 0 and (D[#D] eq 83 where D is PrimeDivisors(n^2-1)) ]; // Klaus Brockhaus, Feb 21 2011

(PARI) is(n)=n=n^2-1; forprime(p=2, 79, n/=p^valuation(n, p)); n>1 && 83^valuation(n, 83)==n \\ Charles R Greathouse IV, Jul 01 2013

CROSSREFS

Cf. A175607, A181447-A181467, A181469-A181470, A181568.

Sequence in context: A296880 A077684 A044982 * A081648 A281921 A303885

Adjacent sequences:  A181465 A181466 A181467 * A181469 A181470 A181471

KEYWORD

fini,nonn

AUTHOR

Artur Jasinski, Oct 21 2010

STATUS

approved

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Last modified November 21 00:10 EST 2019. Contains 329348 sequences. (Running on oeis4.)