cp's OEIS Frontend

A342663 Numerator of ratio A342661(n)/A342662(n): a(n) = A342661(n) / gcd(A342661(n), A342662(n)).

%I A342663 #12 Mar 28 2021 15:53:02
%S A342663 1,2,9,4,10,3,21,8,63,20,22,9,78,7,5,16,119,21,171,40,189,44,115,3,
%T A342663 325,52,81,3,116,5,465,32,33,238,7,9,592,57,351,16,779,63,903,88,35,
%U A342663 115,517,18,1519,650,119,312,424,27,220,14,1539,232,531,5,1830,155,1323,64,260,11,2077,68,345,7,1207,42,2628,1184
%N A342663 Numerator of ratio A342661(n)/A342662(n): a(n) = A342661(n) / gcd(A342661(n), A342662(n)).
%C A342663 Let r(row,col) = A341605(row,col)/A341606(row,col) and d(n) = A342661(n)/A342661(n) = A342663(n)/A342664(n). Then for row > 1, r(row-1,col) = d(A246278(row,col)) * r(row,col).
%H A342663 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%H A342663 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%F A342663 a(n) = A342661(n) / A342670(n) = A342661(n) / gcd(A342661(n), A342662(n)).
%o A342663 (PARI)
%o A342663 A064989(n) = { my(f); f = factor(n); if((n>1 && f[1,1]==2), f[1,2] = 0); for (i=1, #f~, f[i,1] = precprime(f[i,1]-1)); factorback(f) };
%o A342663 A326041(n) = sigma(A064989(n));
%o A342663 A342661(n) = (n*A326041(n));
%o A342663 A342662(n) = (sigma(n)*A064989(n));
%o A342663 A342663(n) = { my(u=A342661(n)); (u/gcd(u, A342662(n))); };
%o A342663 \\ Alternatively as:
%o A342663 A342663(n) = numerator(A342661(n)/A342662(n));
%Y A342663 Cf. A000203, A064989, A246278, A326041, A341526, A341527 [= a(A003961(n))], A341605, A341606, A342661, A342662, A342664 (denominators), A342670.
%K A342663 nonn,frac
%O A342663 1,2
%A A342663 _Antti Karttunen_, Mar 23 2021