A348972 a(n) = gcd(A003959(n), A129283(n)), where A003959 is multiplicative with a(p^e) = (p+1)^e and A129283(n) is sum of n and its arithmetic derivative.

1, 3, 4, 1, 6, 1, 8, 1, 1, 1, 12, 4, 14, 1, 1, 3, 18, 3, 20, 2, 1, 1, 24, 4, 1, 1, 2, 12, 30, 1, 32, 1, 1, 1, 1, 48, 38, 1, 1, 54, 42, 1, 44, 4, 12, 1, 48, 4, 1, 1, 1, 18, 54, 3, 1, 4, 1, 1, 60, 8, 62, 1, 2, 1, 1, 1, 68, 2, 1, 3, 72, 12, 74, 1, 2, 12, 1, 1, 80, 2, 1, 1, 84, 16, 1, 1, 1, 12, 90, 3, 1, 4, 1, 1, 1, 4, 98

Offset

1,2

Links

Table of n, a(n) for n=1..97.

Formula

a(n) = gcd(A003959(n), A129283(n)) = gcd(A003959(n), n+A003415(n)).

a(n) = gcd(A003959(n), A348970(n)) = gcd(A129283(n), A348970(n)).

a(n) = A129283(n) / A348973(n) = A003959(n) / A348974(n).

Mathematica

f1[p_, e_] := e/p; f2[p_, e_] := (p + 1)^e; a[1] = 1; a[n_] := GCD[n*(1 + Plus @@ f1 @@@ (f = FactorInteger[n])), Times @@ f2 @@@ f]; Array[a, 100] (* Amiram Eldar, Nov 06 2021 *)

Prog

(PARI)
A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A003959(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1]++); factorback(f); };
A348972(n) = gcd(A003959(n), (n+A003415(n)));

Crossrefs

Cf. A003415, A003959, A129283, A348970, A348973, A348974.

Cf. also A343226.

Sequence in context: A019599 A177971 A114156 * A354718 A339964 A342915

Adjacent sequences: A348969 A348970 A348971 * A348973 A348974 A348975

Keyword

nonn

Author

Antti Karttunen, Nov 06 2021

Status

approved