A348036 a(n) = gcd(n, A003968(n)), where A003968 is multiplicative with a(p^e) = p*(p+1)^(e-1).

1, 2, 3, 2, 5, 6, 7, 2, 3, 10, 11, 6, 13, 14, 15, 2, 17, 6, 19, 10, 21, 22, 23, 6, 5, 26, 3, 14, 29, 30, 31, 2, 33, 34, 35, 36, 37, 38, 39, 10, 41, 42, 43, 22, 15, 46, 47, 6, 7, 10, 51, 26, 53, 6, 55, 14, 57, 58, 59, 30, 61, 62, 21, 2, 65, 66, 67, 34, 69, 70, 71, 72, 73, 74, 15, 38, 77, 78, 79, 10, 3, 82, 83, 42

Offset

1,2

Links

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

Formula

a(n) = gcd(n, A003968(n)).

a(n) = gcd(n, A348030(n)) = gcd(A003968(n), A348030(n)).

a(n) = n / A348037(n) = A003968(n) / A348038(n).

a(n) = A007947(n) * A348039(n).

Mathematica

f[p_, e_] := p*(p + 1)^(e - 1); a[n_] := GCD[n, Times @@ f @@@ FactorInteger[n]]; Array[a, 100] (* Amiram Eldar, 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); }
A348036(n) = gcd(n, A003968(n));

Crossrefs

Differs from A007947 at the positions given by A347960.

Cf. A003959, A003968, A348030, A348037, A348038, A348039.

Sequence in context: A062953 A347230 A015052 * A053166 A166140 A019555

Adjacent sequences: A348033 A348034 A348035 * A348037 A348038 A348039

Keyword

nonn

Author

Antti Karttunen, Oct 19 2021

Status

approved