A322320 a(n) = gcd(A003557(n), A173557(n)).

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 4, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 3, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 4, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 4, 1

Offset

1,12

Links

Antti Karttunen, Table of n, a(n) for n = 1..20000

Formula

a(n) = gcd(A003557(n), A173557(n)) = gcd(A322351(n), A322352(n)).

a(n) = A000010(n) / A322321(n).

Mathematica

a[n_] := If[n == 1, 1, Module[{f=FactorInteger[n]}, GCD[ Times@@ (First[#] ^(Last[#]-1)& /@  f), Times@@((#-1)& @@@ f)]]]; Array[a, 120] (* Amiram Eldar, Dec 05 2018 *)

Prog

(PARI)
A003557(n) = { my(f=factor(n)); for (i=1, #f~, f[i, 2] = f[i, 2]-1); factorback(f); }; \\ From A003557
A173557(n) = factorback(apply(p -> p-1, factor(n)[, 1]));
A322320(n) = gcd(A173557(n), A003557(n));

Crossrefs

Cf. A000010, A003557, A173557, A322321, A322351, A322352.

Cf. also A066086, A322318.

Sequence in context: A316439 A335078 A086597 * A369008 A238015 A257679

Adjacent sequences: A322317 A322318 A322319 * A322321 A322322 A322323

Keyword

nonn

Author

Antti Karttunen, Dec 05 2018

Status

approved