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Search: id:A057660
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| A057660 |
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Sum_{k=1..n} n/g.c.d.(n,k). |
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+0
27
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| 1, 3, 7, 11, 21, 21, 43, 43, 61, 63, 111, 77, 157, 129, 147, 171, 273, 183, 343, 231, 301, 333, 507, 301, 521, 471, 547, 473, 813, 441, 931, 683, 777, 819, 903, 671, 1333, 1029, 1099, 903, 1641, 903, 1807, 1221, 1281, 1521, 2163, 1197, 2101, 1563, 1911, 1727
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Also sum of the orders of the elements in a cyclic group with n elements - Avi Peretz (njk(AT)netvision.net.il), Mar 31 2001
Also inverse Moebius transform of EulerPhi[n^2].
Sequence is multiplicative, e.g. a(10) = a(2)*a(5) = 3*21 = 63.
a(n) = sigma[2,n^2]/sigma[1,n^2] = A001157[A000290(n)]/A000203[A000290(n)] = A001157[A000290(n)]/A065764[n]. - Labos E. (labos(AT)ana.sote.hu), Nov 21 2001
Multiplicative with a(p^e) = (p^(2*e+1)+1)/(p+1).
Equals A054522 * [1, 2, 3,...]. - Gary W. Adamson (qntmpkt(AT)yahoo.com), May 21 2008
Row sums of triangle A054531. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Aug 12 2009]
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REFERENCES
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D. M. Burton, Elementary Number Theory, Allyn and Bacon Inc., Boston MA, 1976, p. 152.
H. W. Gould and Temba Shonhiwa, Indian J. Math. (Allahabad), 39 (1997), 11-35.
H. W. Gould and Temba Shonhiwa, Indian J. Math. (Allahabad), 39 (1997), 183-194.
Walther Janous, Problem 10829, Amer. Math. Monthly, 107 (2000), p. 753.
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..1000
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FORMULA
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Sum of d times phi(d) for all divisors d of n, where phi is Euler's phi function.
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MATHEMATICA
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Table[ DivisorSigma[ 2, n^2 ]/[ DivisorSigma[ 1, n^2 ], {n, 1, 128} ]
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PROGRAM
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(PARI) a(n)=if(n<1, 0, sumdiv(n, d, d*eulerphi(d)))
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CROSSREFS
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Cf. A018804, A051193, A057661, A001157, A000290, A000203, A065764.
Cf. A054522.
Sequence in context: A050577 A095352 A061258 this_sequence A130972 A151923 A067498
Adjacent sequences: A057657 A057658 A057659 this_sequence A057661 A057662 A057663
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KEYWORD
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easy,nice,nonn,mult
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AUTHOR
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Henry W. Gould (gould(AT)math.wvu.edu), Oct 15 2000
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EXTENSIONS
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More terms from James A. Sellers (sellersj(AT)math.psu.edu), Oct 16 2000
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