A088839 Numerator of sigma(4n)/sigma(n).

7, 5, 7, 31, 7, 5, 7, 21, 7, 5, 7, 31, 7, 5, 7, 127, 7, 5, 7, 31, 7, 5, 7, 21, 7, 5, 7, 31, 7, 5, 7, 85, 7, 5, 7, 31, 7, 5, 7, 21, 7, 5, 7, 31, 7, 5, 7, 127, 7, 5, 7, 31, 7, 5, 7, 21, 7, 5, 7, 31, 7, 5, 7, 511, 7, 5, 7, 31, 7, 5, 7, 21, 7, 5, 7, 31, 7, 5, 7, 127, 7, 5, 7, 31, 7, 5, 7, 21, 7, 5, 7, 31

Offset: 1

Author

Labos Elemer, Nov 04 2003

Keywords

• easy
• nonn
• frac

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16384
• Index entries for sequences related to sigma(n).

Crossrefs

For denominator see A088840.

Cf. A000203, A038712, A088837, A088838, A088841, A080278, A193553.

Cf. A006519, A065442, A096268.

Programs

Maple

f:= proc(n) local m;
  m:= padic:-ordp(n,2);
  if m::odd then (2^(m+3)-1)/3 else 2^(m+3)-1 fi
end proc:
map(f, [$1..200]); # Robert Israel, Nov 19 2017

Mathematica

k=4; Table[Numerator[DivisorSigma[1, k*n]/DivisorSigma[1, n]], {n, 1, 128}]

PARI

A088839(n) = numerator(sigma(4*n)/sigma(n)); \\ Antti Karttunen, Nov 18 2017

Formula

a(n) = (8*A006519(n)-1)/(1+2*A096268(n)). - Robert Israel, Nov 19 2017

From Amiram Eldar, Jan 06 2023: (Start)

a(n) = numerator(A193553(n)/A000203(n)).

Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k)/A088840(k) = 3*A065442 + 1 = 5.820085... . (End)

Extensions

Typo in definition corrected by Antti Karttunen, Nov 18 2017