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A344484
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a(n) = Sum_{d|n} d^phi(n/d).
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1
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1, 3, 4, 7, 6, 14, 8, 17, 19, 32, 12, 48, 14, 86, 122, 57, 18, 137, 20, 328, 800, 1058, 24, 250, 651, 4136, 838, 4252, 30, 1804, 32, 625, 59204, 65588, 18062, 4557, 38, 262202, 531650, 5394, 42, 51790, 44, 1049788, 29018, 4194374, 48, 8906, 117699, 1059277, 43047062
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OFFSET
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1,2
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COMMENTS
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If p is prime, a(p) = Sum_{d|p} d^phi(p/d) = 1^(p-1) + p^1 = p + 1.
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LINKS
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EXAMPLE
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a(6) = Sum_{d|6} d^phi(6/d) = 1^phi(6) + 2^phi(3) + 3^phi(2) + 6^phi(1) = 14.
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MATHEMATICA
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Table[Sum[k^EulerPhi[n/k^(1 - Ceiling[n/k] + Floor[n/k])] (1 - Ceiling[n/k] + Floor[n/k]), {k, n}], {n, 80}]
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PROG
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(PARI) a(n) = sumdiv(n, d, d^eulerphi(n/d)); \\ Michel Marcus, May 21 2021
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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