cp's OEIS Frontend

A098229 a(n) = 6*c(m,1) where m = A003586(n) is the n-th 3-smooth number, c(m,k) = {(m^(2*k)-1)*B(2*k)}, {x} denotes the fractional part of x and B(k) is the k-th Bernoulli number.

%I A098229 #15 May 03 2025 07:46:03
%S A098229 0,3,2,3,5,3,2,5,3,5,5,2,3,5,5,5,3,5,2,5,5,3,5,5,5,5,2,3,5,5,5,5,5,3,
%T A098229 5,5,2,5,5,5,3,5,5,5,5,5,5,3,2,5,5,5,5,5,5,3,5,5,5,5,5,2,5,5,3,5,5,5,
%U A098229 5,5,5,5,5,3,5,5,2,5,5,5,5,5,5,3,5,5,5,5,5,5,5,5,2,5,3,5,5,5,5,5,5,5,5,5,5
%N A098229 a(n) = 6*c(m,1) where m = A003586(n) is the n-th 3-smooth number, c(m,k) = {(m^(2*k)-1)*B(2*k)}, {x} denotes the fractional part of x and B(k) is the k-th Bernoulli number.
%C A098229 If m is a 3-smooth number (i.e., of form 2^i*3^j for i,j >= 0), the value of c(m,k) is independent of k.
%H A098229 Amiram Eldar, <a href="/A098229/b098229.txt">Table of n, a(n) for n = 1..10000</a>
%F A098229 a(1) = 0; for k > 0, a(2^k) = 3 and a(3^k) = 2; for i > 0 and j > 0, a(2^i*3^j) = 5.
%t A098229 s[n_] := If[Times @@ ({2, 3}^IntegerExponent[n, {2, 3}]) == n, 6 * FractionalPart[(n^2-1)/6], Nothing]; Array[s, 125000] (* _Amiram Eldar_, May 03 2025 *)
%o A098229 (PARI) m=7;for(n=1,1000000,if(gcd(n,6^100)==n,print1(6*frac((n^(2*m)-1)*bernfrac(2*m)),",")))
%Y A098229 Cf. A003586, A027641, A027642.
%K A098229 nonn
%O A098229 1,2
%A A098229 _Benoit Cloitre_, Oct 25 2004