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.

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.

Links

Antti Karttunen, Table of n, a(n) for n = 1..8191

Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537

Index entries for sequences computed from indices in prime factorization

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

Adjacent sequences: A340069 A340070 A340071 * A340073 A340074 A340075

Keyword

nonn

Author

Antti Karttunen, Dec 28 2020

Status

approved