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A181466
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Numbers n such that 73 is the largest prime factor of n^2-1.
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3
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72, 74, 145, 147, 218, 220, 291, 293, 364, 439, 512, 729, 731, 804, 875, 1021, 1023, 1167, 1169, 1240, 1313, 1315, 1459, 1461, 1607, 1678, 1680, 1751, 1826, 1899, 2045, 2116, 2262, 2481, 2483, 2554, 2702, 2773, 2848, 3067, 3284, 3359, 3576, 3649, 3722
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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(21) = 4573663454608289; primepi(73) = 21.
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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 == 73, AppendTo[rr, n]]]; n++ ]; rr (* Artur Jasinski *)
Select[Range[300000], FactorInteger[#^2-1][[-1, 1]]==73&]
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PROG
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(Magma) [ n: n in [2..300000] | m eq 73 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 73 where D is PrimeDivisors(n^2-1)) ]; // Klaus Brockhaus, Feb 21 2011
(PARI) is(n)=n=n^2-1; forprime(p=2, 71, n/=p^valuation(n, p)); n>1 && 73^valuation(n, 73)==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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