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A347100
a(n) = phi(A003961(n)) - phi(n), where A003961 is the prime shift towards larger primes, and phi is Euler totient function.
3
0, 1, 2, 4, 2, 6, 4, 14, 14, 8, 2, 20, 4, 14, 16, 46, 2, 34, 4, 28, 28, 14, 6, 64, 22, 20, 82, 48, 2, 40, 6, 146, 28, 20, 36, 108, 4, 26, 40, 92, 2, 68, 4, 52, 96, 34, 6, 200, 68, 64, 40, 72, 6, 182, 32, 156, 52, 32, 2, 128, 6, 42, 164, 454, 48, 76, 4, 76, 68, 96, 2, 336, 6, 44, 128, 96, 60, 104, 4, 292, 446, 44, 6
OFFSET
1,3
COMMENTS
Möbius transform of A336853.
FORMULA
a(n) = A003972(n) - A000010(n).
a(n) = A337549(n) + A051953(n).
a(n) = Sum_{d|n} A008683(n/d) * A336853(d).
For all n >= 1, a(A000040(n)) = A001223(n).
MATHEMATICA
f[p_, e_] := NextPrime[p]^e; a[n_] := EulerPhi[Times @@ f @@@ FactorInteger[n]] - EulerPhi[n]; Array[a, 100] (* Amiram Eldar, Nov 27 2021 *)
PROG
(PARI) A347100(n) = { my(f=factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); (eulerphi(factorback(f))-eulerphi(n)); };
(PARI)
A336853(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); (factorback(f)-n); };
A347100(n) = sumdiv(n, d, moebius(n/d)*A336853(d));
CROSSREFS
Möbius transform of A336853.
Cf. also A346249, A347098.
Sequence in context: A374456 A340148 A049200 * A164701 A325965 A198540
KEYWORD
nonn
AUTHOR
Antti Karttunen, Aug 19 2021
STATUS
approved