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 A341525 #16 Dec 28 2024 09:12:12
%S A341525 1,4,6,13,8,8,12,40,31,32,14,26,18,16,48,121,20,124,24,104,72,56,30,
%T A341525 16,57,24,156,52,32,64,38,364,84,80,96,403,42,32,108,320,44,96,48,14,
%U A341525 248,40,54,242,133,76,24,26,60,208,16,160,144,128,62,208,68,152,372,1093,144,112,72,260,36,128,74,248,80,56
%N A341525 Numerator of A003973(n) / A003961(n).
%C A341525 Also numerator of the ratio (A341528(n)/A341529(n)) / (n/sigma(n)).
%H A341525 Antti Karttunen, <a href="/A341525/b341525.txt">Table of n, a(n) for n = 1..16383</a>
%H A341525 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>.
%H A341525 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>.
%F A341525 a(n) = A017665(A003961(n)).
%F A341525 a(n) = A003973(n) / A336850(n) = A003973(n) / gcd(A003961(n), A003973(n)).
%F A341525 Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} A341525(k)/A336849(k) = 1 / Product_{p prime} (1 - 1/(p*nextprime(p))) = 1.3766054560..., where nextprime(p) = A151800(p). - _Amiram Eldar_, Dec 28 2024
%t A341525 f[p_, e_] := (p^(e + 1) - 1)/((p - 1)*p^e); g[p_, e_] := f[NextPrime[p], e]; a[1] = 1; a[n_] := Numerator[Times @@ g @@@ FactorInteger[n]]; Array[a, 100] (* _Amiram Eldar_, Feb 17 2021 *)
%o A341525 (PARI)
%o A341525 A003961(n) = { my(f=factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); }; \\ From A003961
%o A341525 A341525(n) = { my(u=A003961(n), s=sigma(u)); (s/gcd(u, s)); };
%Y A341525 Cf. A000203, A000290 (positions of odd terms), A003961, A003973, A017665, A151800, A336850, A341526, A341527, A341528, A341529, A341530.
%Y A341525 Cf. A336849 (denominators).
%K A341525 nonn,frac
%O A341525 1,2
%A A341525 _Antti Karttunen_, Feb 16 2021