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A307742 Quasi-logarithm A064097(n) of von Mangoldt's exponential function A014963(n). 4
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 (list; graph; refs; listen; history; text; internal format)
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 A166514

Adjacent sequences:  A307739 A307740 A307741 * A307743 A307744 A307745

KEYWORD

nonn

AUTHOR

I. V. Serov, Apr 26 2019

STATUS

approved

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Last modified September 23 16:41 EDT 2020. Contains 337315 sequences. (Running on oeis4.)