A181452 Numbers k such that 17 is the largest prime factor of k^2 - 1.

16, 33, 35, 50, 67, 69, 101, 103, 118, 120, 169, 188, 239, 271, 307, 339, 441, 511, 545, 577, 749, 883, 1121, 1189, 1376, 1429, 1665, 1871, 2024, 2177, 2311, 2449, 2549, 3401, 4115, 4861, 4999, 5201, 9827, 11663, 24751, 28799, 57121, 62425, 74359, 388961, 672281

Offset: 1

Author

Artur Jasinski, Oct 21 2010

Keywords

• fini
• full
• nonn

Comments

Numbers k such that A076605(k) = 17.

Sequence is finite, for proof see A175607.

Search for terms can be restricted to the range from 2 to A175607(7) = 672281; primepi(17) = 7.

Links

• Artur Jasinski, Table of n, a(n) for n = 1..47

Crossrefs

Cf. A076605, A175607, A181447-A181451, A181453-A181470, A181568.

Programs

Magma

[ n: n in [2..350000] | m eq 17 where m is D[#D] where D is PrimeDivisors(n^2-1) ]; // Klaus Brockhaus, Feb 19 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..700000] | p mod (n^2-1) eq 0 and (D[#D] eq 17 where D is PrimeDivisors(n^2-1)) ]; // Klaus Brockhaus, Feb 24 2011

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 < 700000, If[GCD[jj, n^2 - 1] == n^2 - 1, k = FactorInteger[n^2 - 1]; kk = Last[k][[1]]; If[kk == 17, AppendTo[rr, n]]]; n++ ]; rr (* Artur Jasinski *)
Select[Range[680000], FactorInteger[#^2-1][[-1, 1]]==17&]

PARI

is(n)=n=n^2-1; forprime(p=2, 13, n/=p^valuation(n, p)); n>1 && 17^valuation(n, 17)==n \\ Charles R Greathouse IV, Jul 01 2013