OFFSET
1,49
COMMENTS
7-adic valuation of n.
LINKS
Harvey P. Dale, Table of n, a(n) for n = 1..1000
Dario T. de Castro, P-adic Order of Positive Integers via Binomial Coefficients, INTEGERS, Electronic J. of Combinatorial Number Theory, Vol. 22, Paper A61, 2022.
FORMULA
G.f.: Sum_{k>=1} x^(7^k)/(1-x^(7^k)). See A112765. - Wolfdieter Lang, Jun 18 2014
If n == 0 (mod 7) then a(n) = 1 + a(n/7), otherwise a(n) = 0. - M. F. Hasler, Mar 05 2020
Asymptotic mean: lim_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 1/6. - Amiram Eldar, Jan 17 2022
a(n) = 7*Sum_{j=1..floor(log(n)/log(7))} frac(binomial(n, 7^j)*7^(j-1)/n). - Dario T. de Castro, Jul 12 2022
EXAMPLE
n=147 = 3*7*7 is divisible by 7^2, so a(147)=2.
MAPLE
seq(padic:-ordp(n, 7), n=1..100); # Robert Israel, Mar 05 2020
MATHEMATICA
mek[n_]:=Module[{k=Ceiling[Log[7, n]]}, While[!Divisible[n, 7^k], k--]; k]; Array[ mek, 140] (* Harvey P. Dale, Mar 27 2017 *)
IntegerExponent[Range[150], 7] (* Suggested by Amiram Eldar *) (* Harvey P. Dale, Mar 07 2020 *)
PROG
(PARI) a(n)=valuation(n, 7) \\ Charles R Greathouse IV, Jul 17 2012
(PARI) A=vector(1000); for(i=1, log(#A+.5)\log(7), forstep(j=7^i, #A, 7^i, A[j]++)); A \\ Charles R Greathouse IV, Jul 17 2012
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Redjan Shabani, Jul 16 2012
STATUS
approved