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A306411
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a(n) = phi(n^6) = n^5*phi(n).
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3
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1, 32, 486, 2048, 12500, 15552, 100842, 131072, 354294, 400000, 1610510, 995328, 4455516, 3226944, 6075000, 8388608, 22717712, 11337408, 44569782, 25600000, 49009212, 51536320, 141599546, 63700992, 195312500, 142576512, 258280326, 206524416, 574312172, 194400000, 858874530, 536870912, 782707860, 726966784
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OFFSET
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1,2
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COMMENTS
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The number of elements of the wreath product of C_n and S_6 with cycle partition equal to (6*n) is equal to 5!*a(n), where C_n is the cyclic group of order n, S_6 the symmetric group on 6 elements. - Josaphat Baolahy, Mar 13 2024
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LINKS
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FORMULA
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Multiplicative with a(p^e) = (p - 1)*p^(6*e-1).
Dirichlet g.f.: zeta(s - 6) / zeta(s - 5).
Sum_{k=1..n} a(k) ~ 6*n^7 / (7*Pi^2). See A239443 for a more general formula.
Sum_{k>=1} 1/a(k) = Product_{primes p} (1 + p/(p^7 - p^6 - p + 1)) = 1.03396580456393429553879930771676667947490034699829164744357501993310897305... - Vaclav Kotesovec, Sep 20 2020
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MATHEMATICA
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PROG
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(PARI) a(n) = n^5 * eulerphi(n)
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CROSSREFS
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KEYWORD
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nonn,easy,mult
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AUTHOR
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STATUS
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approved
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