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A181453
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Numbers n such that 19 is the largest prime factor of n^2 - 1.
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3
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18, 20, 37, 39, 56, 77, 113, 134, 151, 153, 170, 191, 246, 265, 305, 324, 341, 362, 379, 417, 419, 571, 626, 647, 664, 685, 721, 799, 911, 951, 989, 1025, 1616, 1937, 2431, 2661, 2889, 3041, 3079, 3212, 3457, 3970, 4751, 4863, 5851, 6271, 6499, 8399
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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(8) = 23718421; primepi(19) = 8.
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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 < 24000000, If[GCD[jj, n^2 - 1] == n^2 - 1, k = FactorInteger[n^2 - 1]; kk = Last[k][[1]]; If[kk == 19, AppendTo[rr, n]]]; n++ ]; rr
Select[Range[300000], FactorInteger[#^2-1][[-1, 1]]==19&]
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PROG
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(Magma) [ n: n in [2..300000] | m eq 19 where m is D[#D] where D is PrimeDivisors(n^2-1) ]; // Klaus Brockhaus, Feb 18 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..24000000] | p mod (n^2-1) eq 0 and (D[#D] eq 19 where D is PrimeDivisors(n^2-1)) ]; // Klaus Brockhaus, Feb 24 2011
(PARI) is(n)=n=n^2-1; forprime(p=2, 17, n/=p^valuation(n, p)); n>1 && 19^valuation(n, 19)==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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