A348039 a(n) = gcd(A003557(n), A327564(n)).

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 6, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 12, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 6

Offset

1,36

Comments

There is interesting regularity in the scatter plot.

Links

Antti Karttunen, Table of n, a(n) for n = 1..65537

Formula

a(n) = gcd(A003557(n), A327564(n)).

a(n) = A348036(n) / A007947(n).

a(n) = A003557(n) / A348037(n).

a(n) = A327564(n) / A348038(n).

Mathematica

{1}~Join~Array[GCD @@ Map[Times @@ # &, Transpose@ Map[{#1^(#2 - 1), (#1 + 1)^(#2 - 1)} & @@ # &, FactorInteger[#]]] &, 105, 2] (* Michael De Vlieger, Oct 20 2021 *)

Prog

(PARI)
A003968(n) = {my(f=factor(n)); for (i=1, #f~, p= f[i, 1]; f[i, 1] = p*(p+1)^(f[i, 2]-1); f[i, 2] = 1); factorback(f); }
A007947(n) = factorback(factorint(n)[, 1]);
A348036(n) = gcd(n, A003968(n));
A348039(n) = (A348036(n)/A007947(n));
(PARI)
A003557(n) = (n/factorback(factorint(n)[, 1]));
A327564(n) = { my(f=factor(n)); for(k=1, #f~, f[k, 1]++; f[k, 2]--); factorback(f); }; \\ From A327564
A348039(n) = gcd(A003557(n), A327564(n));

Crossrefs

Cf. A003557, A003959, A003968, A007947, A327564, A348036, A348037, A348038.

Cf. A347960 (positions of terms > 1).

Sequence in context: A331277 A369458 A257936 * A143532 A348947 A267426

Adjacent sequences: A348036 A348037 A348038 * A348040 A348041 A348042

Keyword

nonn,look

Author

Antti Karttunen, Oct 19 2021

Status

approved