A361707 Moebius transform applied twice to primes.
2, -1, 1, 3, 7, 5, 13, 8, 15, 9, 27, 10, 37, 11, 23, 22, 55, 8, 63, 18, 37, 19, 79, 12, 77, 21, 62, 32, 105, -5, 123, 44, 73, 23, 101, 23, 153, 31, 83, 44, 175, 7, 187, 60, 84, 35, 207, 38, 195, 20, 113, 72, 237, 18, 181, 76, 133, 55, 273, 34, 279, 41, 148, 102, 217
Offset: 1
Links
- Winston de Greef, Table of n, a(n) for n = 1..10000
- N. J. A. Sloane, Transforms
Programs
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Maple
a:= (proc(p) proc(n) uses numtheory; add(p(d)*mobius(n/d), d=divisors(n)) end end@@2)(ithprime): seq(a(n), n=1..100); # Alois P. Heinz, Mar 23 2023 -
Mathematica
A007427[n_] := Sum[MoebiusMu[n/d] MoebiusMu[d], {d, Divisors[n]}]; a[n_] := Sum[A007427[n/d] Prime[d], {d, Divisors[n]}]; Table[a[n], {n, 1, 65}]
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PARI
A007427(n) = if( n<1, 0, direuler(p=2, n, (1 - 'x)^2)[n]) \\ from Michael Somos, Nov 15 2002 A361707(n)=sumdiv(n, d, A007427(n/d) * prime(d)) \\ Winston de Greef, Mar 23 2023
Formula
a(n) = Sum_{d|n} A007427(n/d) * prime(d).