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 A070251 #21 Jan 17 2025 19:28:39
%S A070251 1,1,1,1,1,4,1,6,6,192,1,720,1,23040,6480,10080,1,12902400,1,34836480,
%T A070251 2449440,1857945600,1,50295168000,3000,980995276800,9797760,
%U A070251 9564703948800,1,1518492398911488000,1,41845579776000,1571364748800
%N A070251 Unrelated-factorial numbers: product of numbers unrelated to n (numbers which have a common divisor with n but do not divide n).
%C A070251 a(p) = 1 if p is a prime. 4 is the only composite number such that a(4) = 1.
%C A070251 From _Michael De Vlieger_, Jan 15 2025: (Start)
%C A070251 Conjecture: a(n) is in A055932, and also often in A025487.
%C A070251 Conjectures: a(6) = 4 is likely the only powerful term that exceeds 1. a(8) = a(9) = 6 is likely the only squarefree number exceeding 1 that appears in the sequence.
%C A070251 Conjecture: For n = 2*p, p > 3, gcd(n, a(n)) > 1, rad(n) does not divide a(n), and rad(a(n)) does not divide n, since gpf(n) does not divide a(n). For composite n > 9 not an even squarefree semiprime, n divides a(n). (End)
%H A070251 Michael De Vlieger, <a href="/A070251/b070251.txt">Table of n, a(n) for n = 1..629</a>
%H A070251 Michael De Vlieger, <a href="/A070251/a070251.png">Log log scatterplot of log_10(a(n))</a>, n = 1..10000, where gold represents proper prime power n, green represents squarefree composite n, bright green represents n in A002110, blue represents n in A332785, and purple represents powerful n that are not prime powers.
%H A070251 Michael De Vlieger, <a href="/A070251/a070251_1.png">Plot p^m | a(n) at (x,y) = (n, pi(p))</a>, n = 1..2048, with a color function showing m = 1 in black, m = 2 in red, ..., maximum m in magenta.
%F A070251 a(n) = A055067(n)/A001783(n). - _Vladeta Jovovic_, May 06 2002
%F A070251 From _Michael De Vlieger_, Jan 15 2025: (Start)
%F A070251 Let S(n) = { k < n : 1 < gcd(k,n) < k } = row n of A133995 for composite n > 4.
%F A070251 a(n) = product of S(n).
%F A070251 pi(gpf(a(n))) <= pi(n/lpf(n)), i.e., A000720(A006530(a(n))) <= A000720(n/A020639(n)). (End)
%e A070251 Table of a(n) for composite n <= 30, showing prime power decomposition by listing exponents of primes shown in the column heads:
%e A070251 n a(n) 2 3 5 7 11 13
%e A070251 ---------------------------------------------
%e A070251 6 4 2
%e A070251 8 6 1, 1
%e A070251 9 6 1, 1
%e A070251 10 192 6, 1
%e A070251 12 720 4, 2, 1
%e A070251 14 23040 9, 2, 1
%e A070251 15 6480 4, 4, 1
%e A070251 16 10080 5, 2, 1, 1
%e A070251 18 12902400 13, 2, 2, 1
%e A070251 20 34836480 12, 5, 1, 1
%e A070251 21 2449440 5, 7, 1, 1
%e A070251 22 1857945600 17, 4, 2, 1
%e A070251 24 50295168000 10, 6, 3, 2, 1
%e A070251 25 3000 3, 1, 3
%e A070251 26 980995276800 21, 5, 2, 1, 1
%e A070251 27 9797760 7, 7, 1, 1
%e A070251 28 9564703948800 19, 6, 2, 1, 1, 1
%e A070251 30 1518492398911488000 22,10, 3, 3, 1, 1
%p A070251 A070251 := proc(n) local i;
%p A070251 remove(k->igcd(n,k)=1,{$1..n}); numtheory[divisors](n);
%p A070251 mul(i, i = %% minus % ) end: # _Peter Luschny_, Oct 11 2011
%t A070251 a[n_] := Times @@ Complement[Range[n], Divisors[n]]/Times @@ Select[ Range[n], CoprimeQ[n, #]&];
%t A070251 Array[a, 33] (* _Jean-François Alcover_, Jun 03 2019 *)
%Y A070251 Cf. A045763, A066760, A133995.
%K A070251 nonn
%O A070251 1,6
%A A070251 _Amarnath Murthy_, May 05 2002
%E A070251 More terms from _Vladeta Jovovic_, May 06 2002