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A000082
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n^2*Product_{p|n} (1 + 1/p).
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8
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1, 6, 12, 24, 30, 72, 56, 96, 108, 180, 132, 288, 182, 336, 360, 384, 306, 648, 380, 720, 672, 792, 552, 1152, 750, 1092, 972, 1344, 870, 2160, 992, 1536, 1584, 1836, 1680, 2592, 1406, 2280, 2184, 2880, 1722, 4032, 1892, 3168, 3240, 3312, 2256
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OFFSET
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1,2
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COMMENTS
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For n > 1: A006530(a(n)) = A076566(n-1). - Reinhard Zumkeller, Oct 03 2012
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REFERENCES
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B. Schoeneberg, Elliptic Modular Functions, Springer-Verlag, NY, 1974, p. 79.
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..1000
Index to divisibility sequences
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FORMULA
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Dirichlet g.f.: zeta(s-1)*zeta(s-2)/zeta(2*s-2).
Dirichlet convolution: Sum_{d|n} mu(n/d)*sigma(d^2). - Vladeta Jovovic, Nov 16 2001
Multiplicative with a(p^e) = p^(2*e-1)*(p+1);. - David W. Wilson, Aug 01, 2001.
a(n) = A181797(n)*A003557(n). - R. J. Mathar, Mar 30 2011
a(n) = A001615(n^2). - Enrique Pérez Herrero, Mar 06 2012
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MAPLE
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proc(n) local b, d: b := n^2: for d from 1 to n do if irem(n, d) = 0 and isprime(d) then b := b*(1+d^(-1)): fi: od: RETURN(b): end:
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MATHEMATICA
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Table[ Fold[ If[ Mod[ n, #2 ]==0 && PrimeQ[ #2 ], #1*(1+1/#2), #1 ]&, n^2, Range[ n ] ], {n, 1, 45} ]
Table[ n^2 Times@@(1+1/Select[ Range[ 1, n ], (Mod[ n, #1 ]==0&&PrimeQ[ #1 ])& ]), {n, 1, 45} ]
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PROG
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(PARI) a(n)=if(n<1, 0, direuler(p=2, n, (1+p*X)/(1-p^2*X))[n])
(Haskell)
a000082 n = product $ zipWith (\p e -> p ^ (2*e - 1) * (p + 1))
(a027748_row n) (a124010_row n)
-- Reinhard Zumkeller, Oct 03 2012
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CROSSREFS
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a(n)=n*A001615(n). Cf. A033196.
Cf. A027748, A124010.
Sequence in context: A216453 A119500 A110967 * A106697 A140522 A065218
Adjacent sequences: A000079 A000080 A000081 * A000083 A000084 A000085
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KEYWORD
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nonn,easy,nice,mult
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AUTHOR
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N. J. A. Sloane.
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EXTENSIONS
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Mathematica Program Aug 15 1997 (Olivier Gerard). Additional comments from Michael Somos, May 19, 2000.
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STATUS
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approved
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