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A329071
a(n) = phi(A275314(n)) - mu(A275314(n)), where A275314(n) is Euler's gradus function.
1
0, 2, 3, 3, 5, 2, 7, 2, 5, 1, 11, 5, 13, 4, 7, 5, 17, 1, 19, 7, 6, 4, 23, 1, 6, 5, 7, 6, 29, 4, 31, 1, 13, 6, 11, 7, 37, 8, 7, 4, 41, 3, 43, 13, 6, 8, 47, 7, 13, 3, 19, 7, 53, 4, 7, 3, 11, 9, 59, 6, 61, 16, 11, 7, 17, 5, 67, 19, 20, 4, 71, 4, 73, 17, 11, 11
OFFSET
1,2
FORMULA
a(n) = phi(A275314(n)) - mu(A275314(n)) where phi is Euler's totient function (A000010) and mu is the Mobius function (A008683).
MATHEMATICA
gradus[n_] := 1 + Plus @@ ((First[#] - 1) * Last[#] & /@ FactorInteger[n]); a[n_] := EulerPhi[(g = gradus[n])] - MoebiusMu[g]; Array[a, 76] (* Amiram Eldar, Nov 03 2019 *)
PROG
(PARI) g(n) = my(f = factor(n)); sum(k=1, #f~, (f[k, 1]-1)*f[k, 2])+ 1; \\ A275314
a(n) = my(gn = g(n)); eulerphi(gn) - moebius(gn); \\ Michel Marcus, Nov 04 2019
CROSSREFS
KEYWORD
nonn
AUTHOR
Daniel Hoyt, Nov 03 2019
STATUS
approved