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A340072
a(n) = phi(x) / gcd(x-1, phi(x)), where x = A003961(n), i.e., n with its prime factorization shifted one step towards larger primes.
6
1, 1, 1, 3, 1, 4, 1, 9, 5, 3, 1, 6, 1, 5, 12, 27, 1, 20, 1, 18, 20, 12, 1, 36, 7, 16, 25, 30, 1, 6, 1, 81, 3, 9, 15, 15, 1, 11, 16, 27, 1, 20, 1, 18, 20, 28, 1, 54, 11, 42, 36, 12, 1, 100, 4, 45, 44, 15, 1, 72, 1, 36, 100, 243, 48, 48, 1, 54, 7, 12, 1, 180, 1, 40, 42, 66, 60, 64, 1, 162, 125, 21, 1, 120, 9, 23, 60, 108
OFFSET
1,4
COMMENTS
Prime shifted analog of A160595.
FORMULA
a(n) = A160595(A003961(n)).
a(n) = A003972(n) / A340071(n).
MAPLE
f:= proc(n) local F, x, p, t;
F:= ifactors(n)[2];
x:= mul(nextprime(t[1])^t[2], t=F);
p:= numtheory:-phi(x);
p/igcd(x-1, p)
end proc:
map(f, [$1..100]); # Robert Israel, Dec 28 2020
MATHEMATICA
a[n_] := Module[{x, p, e, phi}, x = Product[{p, e} = pe; NextPrime[p]^e, {pe, FactorInteger[n]}]; phi = EulerPhi[x]; phi/GCD[x-1, phi]];
Array[a, 100] (* Jean-François Alcover, Jan 04 2022 *)
PROG
(PARI)
A003961(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
A340072(n) = { my(x=A003961(n), u=eulerphi(x)); u/gcd(x-1, u); };
CROSSREFS
Cf. A000010, A003961, A003972, A160595, A253885, A340071, A340073, A340075 (gives the odd part).
Cf. also A340082.
Sequence in context: A318841 A300238 A180062 * A079546 A014413 A262072
KEYWORD
nonn
AUTHOR
Antti Karttunen, Dec 28 2020
STATUS
approved