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 A345312 a(n) = Sum_{p|n} (n/p)^gcd(p,n/p). 0
 0, 1, 1, 4, 1, 5, 1, 16, 27, 7, 1, 40, 1, 9, 8, 64, 1, 225, 1, 104, 10, 13, 1, 152, 3125, 15, 729, 200, 1, 31, 1, 256, 14, 19, 12, 2052, 1, 21, 16, 408, 1, 41, 1, 488, 3384, 25, 1, 592, 823543, 100025, 20, 680, 1, 5859, 16, 792, 22, 31, 1, 932, 1, 33, 9270, 1024, 18, 61, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS a(p) = Sum_{p|p} (p/p)^gcd(p,p/p) = 1^1 = 1 for primes p. LINKS Table of n, a(n) for n=1..67. EXAMPLE a(10) = Sum_{p|10} (10/p)^gcd(p,10/p) = 5^gcd(2,5) + 2^gcd(5,2) = 5^1 + 2^1 = 7. MATHEMATICA Table[Sum[(n/k)^GCD[k, n/k] (PrimePi[k] - PrimePi[k - 1]) (1 - Ceiling[n/k] + Floor[n/k]), {k, n}], {n, 100}] CROSSREFS Sequence in context: A028271 A168066 A029666 * A269593 A194512 A131230 Adjacent sequences: A345309 A345310 A345311 * A345313 A345314 A345315 KEYWORD nonn AUTHOR Wesley Ivan Hurt, Jun 13 2021 STATUS approved

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Last modified July 15 12:56 EDT 2024. Contains 374332 sequences. (Running on oeis4.)