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 A381675 #5 Mar 22 2025 19:05:06
%S A381675 4,24,1920,322560,40874803200,25505877196800,23310331287699456000,
%T A381675 31888533201572855808000,108431217215972213061058560000,
%U A381675 2373442412632986039472006832848896000000,8829205774994708066835865418197893120000000,945837910352576904120619801361499836578686566400000000
%N A381675 a(n) = p*2^(p - 1)*(p - 1)!, where p = prime(n).
%C A381675 Let k = 2*prime(n). Then a(n) = product of multiples m*p < k, p|k.
%C A381675 Proper subset of A025487, itself a proper subset of A055932.
%H A381675 Michael De Vlieger, <a href="/A381675/b381675.txt">Table of n, a(n) for n = 1..79</a>
%F A381675 a(n) = Product_{p|k} Product_{m=1..k/p-1} m*p, where k = 2*prime(n).
%F A381675 gpf(a(n)) = prime(n).
%e A381675 Table of n, A100484(n), and a(n) for n = 1..12, showing prime power decomposition via a list of exponents of prime factors:
%e A381675 Exponents of prime factors:
%e A381675 1 1 1 1 2 2 3 3
%e A381675 n 2*prime(n) a(n) 2 3 5 7 1 3 7 9 3 9 1 7
%e A381675 ----------------------------------------------------------
%e A381675 1 4 4 2
%e A381675 2 6 24 3. 1
%e A381675 3 10 1920 7. 1.1
%e A381675 4 14 322560 10. 2.1.1
%e A381675 5 22 40874803200 18. 4.2.1.1
%e A381675 6 26 25505877196800 22. 5.2.1.1.1
%e A381675 7 34 23310331287699456000 31. 6.3.2.1.1.1
%e A381675 8 38 34. 8.3.2.1.1.1.1
%e A381675 9 46 41. 9.4.3.2.1.1.1.1
%e A381675 10 58 53.13.6.4.2.2.1.1.1.1
%e A381675 11 62 56.14.7.4.2.2.1.1.1.1.1
%e A381675 12 74 70.17.8.5.3.2.2.1.1.1.1.1
%e A381675 ----------------------------------------------------------
%e A381675 1 1 1 1 2 2 3 3
%e A381675 2 3 5 7 1 3 7 9 3 9 1 7
%e A381675 a(1) = 4 = 2*2.
%e A381675 a(2) = 24 = (2*4) * 3.
%e A381675 a(3) = 1920 = (2*4*6*8) * 5.
%e A381675 a(4) = 322560 = (2*4*6*8*10*12) * 7, etc.
%t A381675 Table[p = Prime[n]; p*2^(p - 1)*(p - 1)!, {n, 12}]
%Y A381675 Cf. A025487, A055932, A100484, A381674.
%K A381675 nonn,easy
%O A381675 1,1
%A A381675 _Michael De Vlieger_, Mar 15 2025