login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A181470 Numbers n such that 97 is the largest prime factor of n^2 - 1. 27
96, 98, 193, 195, 290, 389, 484, 581, 583, 775, 872, 874, 969, 971, 1066, 1163, 1165, 1359, 1456, 1551, 1553, 1648, 1747, 1844, 1939, 2036, 2133, 2135, 2232, 2521, 2715, 2911, 3008, 3103, 3299, 3394, 3396, 3590, 3976, 4267, 4269, 4463, 4558, 4946, 5045 (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(25) = 99913980938200001; primepi(97) = 25.

LINKS

A. Jasinski, Table of n, a(n) for n = 1..2679

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 == 97, AppendTo[rr, n]]]; n++]; rr

(* or *)

Select[Range[300000], FactorInteger[#^2 - 1][[-1, 1]] == 97 &]

PROG

(MAGMA) [ n: n in [2..300000] | m eq 97 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 97 where D is PrimeDivisors(n^2-1)) ]; // Klaus Brockhaus, Feb 21 2011

(PARI) is(n)=n=n^2-1; forprime(p=2, 89, n/=p^valuation(n, p)); n>1 && 97^valuation(n, 97)==n \\ Charles R Greathouse IV, Jul 01 2013

CROSSREFS

Cf. A175607, A181447-A181469, A181568.

Sequence in context: A090221 A334654 A045528 * A306104 A257411 A175116

Adjacent sequences:  A181467 A181468 A181469 * A181471 A181472 A181473

KEYWORD

fini,full,nonn

AUTHOR

Artur Jasinski, Oct 21 2010

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 1 16:44 EST 2021. Contains 349430 sequences. (Running on oeis4.)