A322357 a(n) = A322354(n) / A322356(n).

1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 3, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 3, 2, 1, 6, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 3, 2, 1, 2, 1, 2, 3, 2, 5, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 6, 1, 2, 1, 2, 1, 6, 1, 2, 1, 2, 1, 2, 1, 2, 3, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 3

Offset

1,2

Links

Antti Karttunen, Table of n, a(n) for n = 1..16384

Antti Karttunen, Data supplement: n, a(n) computed for n = 1..100000

Formula

a(n) = A322354(n) / A322356(n).

Mathematica

f[n_] := If[n == 1, 1, Times @@ Power @@@ ({#[[1]] + 2, #[[2]]} & /@ FactorInteger [n])]; rad[n_] := Times @@ (First@# & /@ FactorInteger@n); fun[p_, n_] := If[ PrimeQ[p + 2] && Divisible[n, p + 2], p + 2, 1]; a[n_] := GCD[rad[n], f[rad[n]]]/ Times @@ (fun[#, n] & /@ FactorInteger[n][[;; , 1]]); Array[a, 120] (* Amiram Eldar, Dec 16 2018 *)

Prog

(PARI)
A166590(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] += 2); factorback(f); };
A322362(n) = gcd(n, A166590(n));
A007947(n) = factorback(factorint(n)[, 1]);
A322354(n) = A322362(A007947(n));
A322356(n) = { my(f = factor(n), m=1); for(i=1, #f~, if(isprime(f[i, 1]+2)&&!(n%(f[i, 1]+2)), m *= (f[i, 1]+2))); (m); };
A322357(n) = (A322354(n)/A322356(n));

Crossrefs

Sequence in context: A167967 A160990 A347516 * A160989 A066788 A160988

Adjacent sequences: A322354 A322355 A322356 * A322358 A322359 A322360

Keyword

nonn

Author

Antti Karttunen, Dec 16 2018

Status

approved