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A065764
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Sum of divisors of square numbers.
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16
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1, 7, 13, 31, 31, 91, 57, 127, 121, 217, 133, 403, 183, 399, 403, 511, 307, 847, 381, 961, 741, 931, 553, 1651, 781, 1281, 1093, 1767, 871, 2821, 993, 2047, 1729, 2149, 1767, 3751, 1407, 2667, 2379, 3937, 1723, 5187, 1893, 4123, 3751, 3871, 2257, 6643
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OFFSET
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1,2
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COMMENTS
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Unlike A065765, the sums of divisors of squares give remainders r=1,3,5 modulo 6: sigma(4)==1,sigma(49)==3, sigma(2401)==5 (mod 6). See also 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(n^2) = A000203(A000290(n)).
Multiplicative with a(p^e) = (p^(2*e+1)-1)/(p-1). - Vladeta Jovovic, Dec 01 2001
Dirichlet g.f. zeta(s)*zeta(s-1)*zeta(s-2)/zeta(2*s-2), inverse Mobius transform of A000082. - R. J. Mathar, Mar 06 2011
Dirichlet convolution of A001157 by the absolute terms of A055615. Also the Dirichlet convolution of A048250 by A000290. - R. J. Mathar, Apr 12 2011
a(n) = Sum{d|n} d*Psi(d), where Psi is A001615. - Enrique Pérez Herrero, Feb 25 2012
a(n) >= (n+1) * sigma(n) - n, where sigma is A000203, equality holds if n is in A000961. - Enrique Pérez Herrero, Apr 21 2012
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MATHEMATICA
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Table[Plus@@Divisors[n^2], {n, 48}] (* Alonso del Arte, Feb 24 2012 *)
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PROG
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(MuPad) numlib::sigma(n^2)$ n=1..81 // Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 13 2008
(Sage) [sigma(n^2, 1)for n in xrange(1, 49)] # From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 13 2009
(PARI) { for (n=1, 10000, write("b065764.txt", n, " ", sigma(n^2)) ) } \\ From Harry J. Smith, Oct 30 2009
(MAGMA) [SumOfDivisors(n^2): n in [1..48]]; // Bruno Berselli, Apr 12 2011
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CROSSREFS
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Cf. A028982, A000203, A000290.
Sequence in context: A096333 A133325 A063583 * A073473 A040084 A151723
Adjacent sequences: A065761 A065762 A065763 * A065765 A065766 A065767
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KEYWORD
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nonn,mult
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AUTHOR
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Labos E. (labos(AT)ana.sote.hu), Nov 19 2001
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STATUS
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approved
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