A181465 Numbers k such that 71 is the largest prime factor of k^2 - 1.

70, 141, 143, 214, 283, 285, 356, 425, 496, 569, 638, 709, 780, 782, 851, 853, 924, 993, 1135, 1208, 1277, 1279, 1561, 1563, 1703, 1847, 2058, 2129, 2131, 2344, 2413, 2626, 2699, 2839, 2841, 3054, 3265, 3267, 3336, 3338, 3409, 3478, 3480, 3551, 3620, 3691

Offset: 1

Author

Artur Jasinski, Oct 21 2010

Keywords

• fini
• full
• nonn

Comments

Numbers k such that A076605(k) = 71.

Sequence is finite, for proof see A175607.

Search for terms can be restricted to the range from 2 to A175607(20) = 238178082107393; primepi(71) = 20.

Links

• Artur Jasinski, Table of n, a(n) for n = 1..1146

Crossrefs

Row 20 of A223701.

Cf. A076605, A175607, A181447-A181464, A181466-A181470, A181568.

Programs

Magma

[ n: n in [2..300000] | m eq 71 where m is D[#D] where D is PrimeDivisors(n^2-1) ]; // Klaus Brockhaus, Feb 19 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 < 14000000, If[GCD[jj, n^2 - 1] == n^2 - 1, k = FactorInteger[n^2 - 1]; kk = Last[k][[1]]; If[kk == 71, AppendTo[rr, n]]]; n++ ]; rr (* Artur Jasinski *)
Select[Range[300000], FactorInteger[#^2-1][[-1, 1]]==71&]

PARI

is(n)=n=n^2-1; forprime(p=2, 67, n/=p^valuation(n, p)); n>1 && 71^valuation(n, 71)==n \\ Charles R Greathouse IV, Jul 01 2013