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A306412
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a(n) = phi(n^8) = n^7*phi(n).
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3
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1, 128, 4374, 32768, 312500, 559872, 4941258, 8388608, 28697814, 40000000, 194871710, 143327232, 752982204, 632481024, 1366875000, 2147483648, 6565418768, 3673320192, 16089691302, 10240000000, 21613062492, 24943578880, 74906159834, 36691771392, 122070312500
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OFFSET
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1,2
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LINKS
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FORMULA
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Multiplicative with a(p^e) = (p - 1)*p^(8*e-1).
Dirichlet g.f.: zeta(s - 8) / zeta(s - 7).
Sum_{k=1..n} a(k) ~ 2*n^9 / (3*Pi^2). See A239443 for a more general formula.
Sum_{n>=1} 1/a(n) = Product_{p prime} (1 + p/(p^9 - p^8 - p + 1)) = 1.00807702579309679541... - Amiram Eldar, Dec 06 2020
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MATHEMATICA
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Table[n^7*EulerPhi[n], {n, 1, 25}] (* Amiram Eldar, Dec 06 2020 *)
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PROG
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(PARI) a(n) = n^7 * 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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