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A065765
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Sum of divisors of twice square numbers.
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6
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3, 15, 39, 63, 93, 195, 171, 255, 363, 465, 399, 819, 549, 855, 1209, 1023, 921, 1815, 1143, 1953, 2223, 1995, 1659, 3315, 2343, 2745, 3279, 3591, 2613, 6045, 2979, 4095, 5187, 4605, 5301, 7623, 4221, 5715, 7137, 7905, 5169, 11115, 5679, 8379, 11253
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OFFSET
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1,1
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COMMENTS
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The sum of divisors of 2m^2 [twice a square] always gives remainder r = 3 modulo 6. See A097022.
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LINKS
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T. D. Noe, Table of n, a(n) for n = 1..10000
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FORMULA
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a(n) = sigma(2*n^2) = A000203(2*A000290(n)).
a(n) = 3*A065766(n).
Sum_{k=1..n} a(k) ~ c * n^3, where c = 12*zeta(3)/Pi^2 = 1.461525... . - Amiram Eldar, Oct 28 2022
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MATHEMATICA
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DivisorSigma[1, 2*Range[50]^2] (* Harvey P. Dale, Sep 06 2015 *)
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PROG
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(PARI) { for (n=1, 10000, write("b065765.txt", n, " ", sigma(2*n^2)) ) } \\ Harry J. Smith, Oct 30 2009
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CROSSREFS
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Cf. A000203, A000290, A002117, A028982, A065766, A097022.
Sequence in context: A176661 A117561 A353679 * A318738 A146853 A183476
Adjacent sequences: A065762 A065763 A065764 * A065766 A065767 A065768
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KEYWORD
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nonn
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AUTHOR
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Labos Elemer, Nov 19 2001
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STATUS
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approved
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