A348974 Denominator of ratio A129283(n) / A003959(n), where A003959 is multiplicative with a(p^e) = (p+1)^e and A129283(n) is sum of n and its arithmetic derivative.

1, 1, 1, 9, 1, 12, 1, 27, 16, 18, 1, 9, 1, 24, 24, 27, 1, 16, 1, 27, 32, 36, 1, 27, 36, 42, 32, 6, 1, 72, 1, 243, 48, 54, 48, 3, 1, 60, 56, 3, 1, 96, 1, 27, 8, 72, 1, 81, 64, 108, 72, 7, 1, 64, 72, 54, 80, 90, 1, 27, 1, 96, 64, 729, 84, 144, 1, 81, 96, 48, 1, 36, 1, 114, 72, 15, 96, 168, 1, 243, 256, 126, 1, 18, 108

Offset

1,4

Links

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

Formula

a(n) = A003959(n) / A348972(n) = A003959(n) / gcd(A003959(n), A129283(n)).

Mathematica

f1[p_, e_] := e/p; f2[p_, e_] := (p + 1)^e; a[n_] := Denominator[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); };
A348974(n) = { my(s=A003959(n)); (s/gcd(s, (n+A003415(n)))); };

Crossrefs

Cf. A003415, A003959, A129283, A348970, A348972, A348973 (numerators).

Cf. also A343227.

Sequence in context: A164791 A107829 A062357 * A061215 A072448 A145966

Adjacent sequences: A348971 A348972 A348973 * A348975 A348976 A348977

Keyword

nonn,frac

Author

Antti Karttunen, Nov 06 2021

Status

approved