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A181457
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Numbers n such that 37 is the largest prime factor of n^2 - 1.
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3
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36, 38, 73, 75, 149, 186, 221, 223, 260, 295, 369, 371, 406, 443, 482, 519, 593, 628, 776, 813, 815, 961, 1000, 1072, 1259, 1331, 1333, 1405, 1407, 1444, 1481, 1701, 1814, 1849, 1886, 1923, 1999, 2071, 2367, 2591, 2663, 2737, 2887, 2959, 3329, 3331, 3403
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OFFSET
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1,1
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COMMENTS
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Sequence is finite, for proof see A175607.
Search for terms can be restricted to the range from 2 to A175607(12) = 9447152318; primepi(37) = 12.
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LINKS
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MATHEMATICA
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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 == 37, AppendTo[rr, n]]]; n++ ]; rr (* Artur Jasinski *)
Select[Range[300000], FactorInteger[#^2-1][[-1, 1]]==37&]
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PROG
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(Magma) [ n: n in [2..300000] | m eq 37 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..50000000] | p mod (n^2-1) eq 0 and (D[#D] eq 37 where D is PrimeDivisors(n^2-1)) ]; // Klaus Brockhaus, Feb 20 2011
(PARI) is(n)=n=n^2-1; forprime(p=2, 31, n/=p^valuation(n, p)); n>1 && 37^valuation(n, 37)==n \\ Charles R Greathouse IV, Jul 01 2013
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CROSSREFS
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KEYWORD
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fini,nonn
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AUTHOR
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STATUS
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approved
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