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 A360326 #16 Feb 04 2023 14:14:44 %S A360326 1,1,2,1,2,2,1,1,3,2,2,2,1,1,4,1,2,3,1,2,2,2,1,2,3,1,4,1,1,4,2,1,4,2, %T A360326 2,3,1,1,2,2,2,2,1,2,6,1,1,2,1,3,4,1,1,4,4,1,2,1,2,4,1,2,3,1,2,4,2,2, %U A360326 2,2,1,3,1,1,6,1,2,2,1,2,5,2,2,2,4,1,2 %N A360326 a(n) is the number of divisors of n that have only prime-indexed prime factors. %C A360326 First differs from A322976 at n = 21. %C A360326 Equivalently, a(n) is the number of divisors of the largest divisor of n that has only prime-indexed prime factors. %C A360326 The asymptotic mean of this sequence is Product_{p in A006450} p/(p-1) > 3. See A076610 for a numerical estimate of the value of this product. %H A360326 Amiram Eldar, <a href="/A360326/b360326.txt">Table of n, a(n) for n = 1..10000</a> %F A360326 a(n) = 1 if and only if n is in A320628. %F A360326 a(n) = A000005(n) if and only if n is in A076610. %F A360326 a(n) = A000005(A360325(n)). %F A360326 Multiplicative with a(p^e) = e+1 if p is a prime-indexed prime (A006450), and 1 otherwise. %t A360326 f[p_, e_] := If[PrimeQ[PrimePi[p]], e+1, 1]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] %o A360326 (PARI) a(n) = {my(f = factor(n), p = f[,1], e = f[,2]); prod(i = 1, #p, if(isprime(primepi(p[i])), e[i]+1, 1));} %Y A360326 Cf. A000005, A006450, A076610, A320628, A322976, A360325, A360327. %K A360326 nonn,mult %O A360326 1,3 %A A360326 _Amiram Eldar_, Feb 03 2023