This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A373217 #32 Jun 28 2025 09:14:35
%S A373217 1,1,1,1,1,1,2,1,1,1,1,1,1,2,1,1,1,1,1,1,2,1,1,1,1,1,1,2,1,1,1,1,1,1,
%T A373217 2,1,1,1,1,1,1,2,1,1,1,1,1,1,3,1,1,1,1,1,1,2,1,1,1,1,1,1,2,1,1,1,1,1,
%U A373217 1,2,1,1,1,1,1,1,2,1,1,1,1,1,1,2,1,1,1,1,1,1,2,1,1,1,1,1,1,3,1,1,1,1,1,1,2
%N A373217 Expansion of Sum_{k>=0} x^(7^k) / (1 - x^(7^k)).
%C A373217 The number of powers of 7 that divide n. - _Amiram Eldar_, Mar 29 2025
%H A373217 Seiichi Manyama, <a href="/A373217/b373217.txt">Table of n, a(n) for n = 1..10000</a>
%F A373217 G.f. A(x) satisfies A(x) = x/(1 - x) + A(x^7).
%F A373217 a(7*n+1) = a(7*n+2) = ... = (7*n+6) = 1 and a(7*n+7) = 1 + a(n+1) for n >= 0.
%F A373217 Multiplicative with a(p^e) = e+1 if p = 7, 1 otherwise.
%F A373217 a(n) = -Sum_{d|n} mu(7*d) * tau(n/d).
%F A373217 a(n) = A214411(n) + 1.
%F A373217 From _Amiram Eldar_, May 29 2024: (Start)
%F A373217 Dirichlet g.f.: (7^s/(7^s-1)) * zeta(s).
%F A373217 Sum_{k=1..n} a(k) ~ (7/6) * n. (End)
%F A373217 G.f.: Sum_{i>=1, j>=0} x^(i*7^j). - _Seiichi Manyama_, Mar 23 2025
%F A373217 a(n) = A214411(7*n). - _R. J. Mathar_, Jun 28 2025
%t A373217 a[n_] := 1 + IntegerExponent[n, 7]; Array[a, 100] (* _Amiram Eldar_, May 29 2024 *)
%o A373217 (PARI) a(n) = valuation(n, 7)+1;
%Y A373217 Cf. A001511, A051064, A055457, A115362, A373216.
%Y A373217 Cf. A000005, A008683, A214411, A373221.
%K A373217 nonn,mult,easy
%O A373217 1,7
%A A373217 _Seiichi Manyama_, May 28 2024