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 A377019 #9 Oct 13 2024 11:17:40
%S A377019 1,2,3,4,5,6,7,9,10,11,12,13,14,15,17,18,19,20,21,22,23,25,26,28,29,
%T A377019 30,31,33,34,35,36,37,38,39,41,42,43,44,45,46,47,49,50,51,52,53,55,57,
%U A377019 58,59,60,61,62,63,64,65,66,67,68,69,70,71,73,74,75,76,77,78
%N A377019 Numbers whose prime factorization has exponents that are all factorial numbers.
%C A377019 First differs from its subsequence A004709 and from A344742 at n = 55: a(55) = 64 = 2^6 is not a term of A004709 and A344742.
%C A377019 Numbers k such that A376885(k) = A001221(k).
%C A377019 The asymptotic density of this sequence is Product_{p prime} (1 - 1/p^3 + (1 - 1/p) * (Sum_{k>=3} 1/p^(k!))) = 0.84018238588352905855... .
%H A377019 Amiram Eldar, <a href="/A377019/b377019.txt">Table of n, a(n) for n = 1..10000</a>
%t A377019 factorialQ[n_] := factorialQ[n] = Module[{m = n, k = 2}, While[Divisible[m, k], m /= k; k++]; m == 1]; q[n_] := AllTrue[FactorInteger[n][[;;, 2]], factorialQ]; Select[Range[100], q]
%o A377019 (PARI) isf(n) = {my(k = 2); while(!(n % k), n /= k; k++); n == 1;}
%o A377019 is(k) = {my(e = factor(k)[, 2]); for(i = 1, #e, if(!isf(e[i]), return(0))); 1;}
%Y A377019 Cf. A000142, A001221, A344742, A376885, A377021, A377022.
%Y A377019 Subsequence of A377020.
%Y A377019 Subsequences: A005117, A004709.
%K A377019 nonn,easy
%O A377019 1,2
%A A377019 _Amiram Eldar_, Oct 13 2024