A181464 Numbers k such that 67 is the largest prime factor of k^2-1.

66, 68, 133, 135, 202, 267, 269, 334, 401, 604, 671, 736, 805, 937, 939, 1004, 1006, 1205, 1272, 1274, 1341, 1473, 1475, 1540, 1609, 1676, 1741, 2078, 2143, 2145, 2210, 2279, 2545, 2547, 2746, 2813, 2815, 2882, 2949, 3081, 3349, 3550, 3552, 3751, 3887

Offset

1,1

Comments

Numbers k such that A076605(k) = 67.

Sequence is finite, for proof see A175607.

Search for terms can be restricted to the range from 2 to A175607(19) = 25640240468751; primepi(67) = 19.

Links

Artur Jasinski, Table of n, a(n) for n = 1..976

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 < 14000000, If[GCD[jj, n^2 - 1] == n^2 - 1, k = FactorInteger[n^2 - 1]; kk = Last[k][[1]]; If[kk == 67, AppendTo[rr, n]]]; n++ ]; rr (* Artur Jasinski *)
Select[Range[300000], FactorInteger[#^2-1][[-1, 1]]==67&]

Prog

(Magma) [ n: n in [2..300000] | m eq 67 where m is D[#D] where D is PrimeDivisors(n^2-1) ]; // Klaus Brockhaus, Feb 19 2011
(PARI) is(n)=n=n^2-1; forprime(p=2, 61, n/=p^valuation(n, p)); n>1 && 67^valuation(n, 67)==n \\ Charles R Greathouse IV, Jul 01 2013

Crossrefs

Cf. A076605, A175607, A181447-A181463, A181465-A181470, A181568.

Sequence in context: A059175 A031960 A376289 * A250739 A124142 A036207

Adjacent sequences: A181461 A181462 A181463 * A181465 A181466 A181467

Keyword

fini,full,nonn

Author

Artur Jasinski, Oct 21 2010

Status

approved