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Search: id:A000113
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| A000113 |
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Number of transformation groups of order n. |
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+0
1
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| 1, 3, 4, 3, 6, 12, 8, 6, 4, 18, 12, 12, 14, 24, 24, 6, 18, 12, 20, 18, 32, 36, 24, 24, 30, 42, 12, 24, 30, 72, 32, 12, 48, 54, 48, 12, 38, 60, 56, 36, 42, 96, 44, 36, 24, 72, 48, 24, 56, 90, 72, 42, 54, 36, 72, 48, 80, 90, 60, 72
(list; graph; listen)
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OFFSET
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1,2
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REFERENCES
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B. Schoeneberg, Elliptic Modular Functions, Springer-Verlag, NY, 1974, p. 139.
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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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Let psi(m) = A001615(m) (Dedekind's psi function). Write n = 2^i*3^j*k, where (6,k) = 1, and let i' = floor(i/2) for i < 6, i' = 3 for i >= 6; let j' = 0 for j = 0 or 1, j' = 1 for j >= 2. Then a(n) = psi(n/(2^i'*3^j')) = psi(n)/(2^i'*3^j').
Multiplicative with a(2^e)=3*2^Floor[(e-1)/2] for 0<e<7, a(2^e)=3*2^(e-4) for e>=7, a(3^e)=4 for 0<e<3, a(3^e)=4*3^(e-2) for e>=3, and a(p^e)=(p+1)*p^(e-1) for p>3. - T. D. Noe (noe(AT)sspectra.com), Nov 14 2006
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CROSSREFS
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Sequence in context: A073181 A046897 A109506 this_sequence A069915 A033634 A111970
Adjacent sequences: A000110 A000111 A000112 this_sequence A000114 A000115 A000116
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KEYWORD
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nonn,easy,mult
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AUTHOR
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njas
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