login
A306694
a(n) is the denominator of log(A014963(n))/log(n) if n > 1 and a(1) = 1.
2
1, 1, 1, 2, 1, 1, 1, 3, 2, 1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 3, 1, 1, 1, 1, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 6, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2
OFFSET
1,4
COMMENTS
Log(A112624(n)) is the inverse Möbius transform of log(a(n)).
FORMULA
If n is a prime power (in the sense of A246655) then a(n) is the exponent of this prime and otherwise a(n) is 1. - Peter Luschny, Mar 18 2019
Dirichlet generating function: zeta(s) + Sum_{n>=1} n*primezeta((n + 1)*s). - Mats Granvik, Mar 24 2019
MAPLE
with(numtheory): pexp := n -> ifactors(n)[2][1][2]:
a := n -> if nops(factorset(n)) = 1 then pexp(n) else 1 fi:
seq(a(n), n=1..101); # Peter Luschny, Mar 19 2019
MATHEMATICA
Table[Denominator[FullSimplify[MangoldtLambda[n]/Log[n]]], {n, 1, 101}]
PROG
(Sage)
def a(n):
F = n.factor()
return 1 if len(F) != 1 else F[0][1]
print([a(n) for n in (1..101)]) # Peter Luschny, Mar 18 2019
(PARI) A306694(n) = if((n=isprimepower(n))>0, n, 1); \\ Antti Karttunen, Nov 17 2019
CROSSREFS
KEYWORD
nonn
AUTHOR
Mats Granvik, Mar 05 2019
EXTENSIONS
Data section extended up to term a(121) by Antti Karttunen, Nov 17 2019
STATUS
approved