A181467 Numbers k such that 79 is the largest prime factor of k^2 - 1.

78, 80, 157, 159, 236, 317, 473, 475, 552, 554, 631, 712, 791, 868, 870, 947, 949, 1026, 1028, 1105, 1184, 1421, 1737, 1739, 1816, 1897, 2053, 2134, 2211, 2213, 2369, 2450, 2529, 2685, 2687, 2843, 2924, 3001, 3161, 3477, 3554, 3870, 3949, 3951, 4186, 4188

Offset: 1

Author

Artur Jasinski, Oct 21 2010

Keywords

• fini
• full
• nonn

Comments

Numbers k such that A076605(k) = 79.

Sequence is finite, for proof see A175607.

Search for terms can be restricted to the range from 2 to A175607(22) = 19182937474703818751; primepi(79) = 22.

Links

• Artur Jasinski, Table of n, a(n) for n = 1..1698

Crossrefs

Row 22 of A223701.

Cf. A076605, A175607, A181447-A181466, A181468-A181470, A181568.

Programs

Magma

[ n: n in [2..300000] | m eq 79 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 79 where D is PrimeDivisors(n^2-1)) ]; // Klaus Brockhaus, Feb 21 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 < 3222617400, If[GCD[jj, n^2 - 1] == n^2 - 1, k = FactorInteger[n^2 - 1]; kk = Last[k][[1]]; If[kk == 79, AppendTo[rr, n]]]; n++ ]; rr (* Artur Jasinski *)
Select[Range[300000], FactorInteger[#^2-1][[-1, 1]]==79&]

PARI

is(n)=n=n^2-1; forprime(p=2, 73, n/=p^valuation(n, p)); n>1 && 79^valuation(n, 79)==n \\ Charles R Greathouse IV, Jul 01 2013