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A241541
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Exponent of 11 in prime factorization of (2^n + 3^n + 5^n + 7^n).
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2
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0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2
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OFFSET
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0,6
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COMMENTS
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11^a(n) is the largest power of 11 dividing (2^n + 3^n + 5^n + 7^n);
(2^n + 3^n + 5^n + 7^n) is divisible by 11^2 = 121 for n == 5 mod 10.
Among first 10000 nonzero terms there are {8182, 1652, 150, 14, 1, 1} terms with values {2, 3, 4, 5, 6, 7}, respectively.
Record values are a(5) = 2, a(45) = 3, a(595) = 5, a(40525) = 7, a(6482565) = 8, a(97435855) = 9, a(927694285) = 10, a(11789738455) = 11, a(129687123005) = 12, a(508958242255) = 13, a(11921425066695) = 14, a(74689992601115) = 15, a(1110371356919045) = 16, a(20886240847078255) = 17, a(229748649317860805) = 18, etc. - Charles R Greathouse IV, Apr 25 2014
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LINKS
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EXAMPLE
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at n = 5, 2^n + 3^n + 5^n + 7^n = 20207 = 11^2*167,
at n = 15, 2^n + 3^n + 5^n + 7^n = 4778093469743 = 11^2*587*67271509.
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MATHEMATICA
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Table[IntegerExponent[2^n + 3^n + 5^n + 7^n, 11], {n, 0, 100}]
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PROG
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(PARI) a(n, e=8)=my(m=11^e, o=valuation(Mod(2, m)^n +Mod(3, m)^n +Mod(5, m)^n +Mod(7, m)^n, 11)); if(o<e, o, a(n, 2*e)) \\ Charles R Greathouse IV, Apr 25 2014
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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