A307742 Quasi-logarithm A064097(n) of von Mangoldt's exponential function A014963(n).

0, 1, 2, 1, 3, 0, 4, 1, 2, 0, 5, 0, 5, 0, 0, 1, 5, 0, 6, 0, 0, 0, 7, 0, 3, 0, 2, 0, 7, 0, 7, 1, 0, 0, 0, 0, 7, 0, 0, 0, 7, 0, 8, 0, 0, 0, 9, 0, 4, 0, 0, 0, 8, 0, 0, 0, 0, 0, 9, 0, 8, 0, 0, 1, 0, 0, 9, 0, 0, 0, 9, 0, 8, 0, 0, 0, 0, 0, 9, 0, 2, 0, 9, 0, 0, 0, 0, 0, 9

Offset

1,3

Links

I. V. Serov, Table of n, a(n) for n = 1..10000

Formula

a(n) = A064097(A014963(n)).

a(n) = 1 + A064097(n-1) if n is prime.

a(n) = a(p) if n=p^k with k > 1.

a(n) = 0 if n is not a prime power or n = 1.

a(n) = -Sum_{d|n} A064097(d)*A008683(d) by Mobius inversion.

Mathematica

qLog[n_] := qLog[n] = Module[{p, e}, If[n == 1, 0, Sum[{p, e} = pe; (1 + qLog[p-1])e, {pe, FactorInteger[n]}]]];
a[n_] := qLog[Exp[MangoldtLambda[n]]];
Array[a, 100] (* Jean-François Alcover, May 07 2019 *)

Prog

(PARI) mang(n) = ispower(n, , &n); if(isprime(n), n, 1); \\ A014963
ql(n) = if (n==1, 0, if(isprime(n), 1+ql(n-1), sumdiv(n, p, if(isprime(p), ql(p)*valuation(n, p))))); \\ A064097
a(n) = ql(mang(n)); \\ Michel Marcus, Apr 26 2019

Crossrefs

Cf. A064097, A014963, A008683, A307743.

Sequence in context: A096269 A260437 A262677 * A297109 A073312 A350941

Adjacent sequences: A307739 A307740 A307741 * A307743 A307744 A307745

Keyword

nonn

Author

I. V. Serov, Apr 26 2019

Status

approved