A342664 Denominator of ratio A342661(n)/A342662(n).

1, 3, 8, 7, 9, 4, 20, 15, 52, 27, 21, 14, 77, 10, 4, 31, 117, 26, 170, 63, 160, 63, 114, 5, 279, 77, 64, 5, 115, 6, 464, 63, 28, 351, 6, 13, 589, 85, 308, 27, 777, 80, 902, 147, 26, 171, 516, 31, 1425, 837, 104, 539, 423, 32, 189, 25, 1360, 345, 530, 7, 1829, 232, 1040, 127, 231, 14, 2074, 117, 304, 9, 1206, 65, 2627

Offset: 1

Author

Antti Karttunen, Mar 23 2021

Keywords

• nonn
• frac

Links

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

Crossrefs

Cf. A000203, A064989, A326041, A341526 [= a(A003961(n))], A341527, A342661, A342662, A342663 (numerators), A342667 [largest prime factor of a(A003961(n))], 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));
A342664(n) = { my(v=A342662(n)); (v/gcd(A342661(n),v)); };
\\ Alternatively as:
A342664(n) = denominator(A342661(n)/A342662(n));

Formula

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