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A273999
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Numbers of the form n^2+1 that divide 4^n-1.
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3
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1, 5, 17, 257, 46657, 65537, 148997, 67371265, 405458497, 1370776577, 3497539601, 4294967297, 80542440001, 422240040001, 1911029760001, 139251776898727937, 286245437364810001, 6017402415698251777, 18446744073709551617
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OFFSET
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1,2
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COMMENTS
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Corresponding values of n are given by A273870(k)-1 for k>=1.
Contains Fermat numbers (A000215) greater than 3.
Also, numbers of the form n^2+1 that divide (4^k)^n-1 for all k >= 0.
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LINKS
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FORMULA
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EXAMPLE
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17 = 4^2+1 is a term because divides 4^4-1; 255 / 17 = 15.
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PROG
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(PARI) is(n) = ceil(sqrt(n-1))==sqrtint(n-1) && Mod(4, n)^(sqrtint(n))==1
for(n=0, 1e12, if(is(n^2+1), print1(n^2+1, ", "))) \\ Felix Fröhlich, Jun 06 2016
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CROSSREFS
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Subsequence of A002522 (numbers of the form n^2+1).
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KEYWORD
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nonn,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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