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

1, 2, 9, 4, 10, 3, 21, 8, 63, 20, 22, 9, 78, 7, 5, 16, 119, 21, 171, 40, 189, 44, 115, 3, 325, 52, 81, 3, 116, 5, 465, 32, 33, 238, 7, 9, 592, 57, 351, 16, 779, 63, 903, 88, 35, 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

Offset: 1

Author

Antti Karttunen, Mar 23 2021

Keywords

• nonn
• frac

Comments

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).

Links

• Index entries for sequences computed from indices in prime factorization
• Index entries for sequences related to sigma(n)

Crossrefs

Cf. A000203, A064989, A246278, A326041, A341526, A341527 [= a(A003961(n))], A341605, A341606, A342661, A342662, A342664 (denominators), A342670.

Programs

PARI

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) };
A326041(n) = sigma(A064989(n));
A342661(n) = (n*A326041(n));
A342662(n) = (sigma(n)*A064989(n));
A342663(n) = { my(u=A342661(n)); (u/gcd(u, A342662(n))); };
\\ Alternatively as:
A342663(n) = numerator(A342661(n)/A342662(n));

Formula

a(n) = A342661(n) / A342670(n) = A342661(n) / gcd(A342661(n), A342662(n)).