The On-Line Encyclopedia of Integer Sequences (OEIS)

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A245785

Denominator of (n/tau(n) + sigma(n)/n)
(history; published version)

#9 by Charles R Greathouse IV at Thu Sep 08 08:46:09 EDT 2022

COMMENTS

First deviation from A245777 (denominator of (n/tau(n) - sigma(n)/n)) is at a(300); a(300) = 25, A245777(300) = 75. Sequence of numbers n such that A245777(n) is not equal to a(n): 300, 768, 1452, 1764, 2100, 3468, 3900, 5376, 5700, 6084, 6348, 9075, 9300, ... See (MAGMAMagma) [n: n in [1..10000] | (Denominator((n/(#[d: d in Divisors(n)]))+(SumOfDivisors(n)/n))) - (Denominator((n/(#[d: d in Divisors(n)]))-(SumOfDivisors(n)/n))) ne 0]

PROG

(MAGMAMagma) [Denominator((n/(#[d: d in Divisors(n)]))+(SumOfDivisors(n)/n)): n in [1..1000]]

Discussion

Thu Sep 08

08:46

OEIS Server: https://oeis.org/edit/global/2944

#8 by N. J. A. Sloane at Fri Aug 15 23:22:38 EDT 2014

STATUS

proposed

approved

#7 by Derek Orr at Fri Aug 15 12:08:53 EDT 2014

STATUS

editing

proposed

#6 by Derek Orr at Fri Aug 15 12:08:51 EDT 2014

PROG

(PARI) for(n=1, 100, s=n/numdiv(n); t=sigma(n)/n; print1(denominator(s+t), ", ")) \\ Derek Orr, Aug 15 2014

STATUS

proposed

editing

#5 by Michel Marcus at Fri Aug 15 10:30:05 EDT 2014

STATUS

editing

proposed

#4 by Michel Marcus at Fri Aug 15 10:29:59 EDT 2014

KEYWORD

nonn,frac,changed

STATUS

proposed

editing

#3 by Jaroslav Krizek at Fri Aug 15 09:44:54 EDT 2014

STATUS

editing

proposed

#2 by Jaroslav Krizek at Fri Aug 15 09:44:32 EDT 2014

NAME

allocated for Jaroslav Krizek

Denominator of (n/tau(n) + sigma(n)/n)

DATA

1, 2, 6, 12, 10, 2, 14, 8, 9, 10, 22, 3, 26, 14, 20, 80, 34, 6, 38, 30, 84, 22, 46, 2, 75, 26, 108, 3, 58, 20, 62, 96, 44, 34, 140, 36, 74, 38, 156, 4, 82, 28, 86, 33, 30, 46, 94, 60, 147, 150, 68, 78, 106, 36, 220, 7, 228, 58, 118, 5, 122, 62, 126, 448, 260

OFFSET

1,2

COMMENTS

Denominator of (n/A000005(n) + A000203(n)/n).

See A245784 - numerator of (n/tau(n) + sigma(n)/n).

A245784(n) / a(n) = integer for numbers n in A245786; a(n) = 1.

First deviation from A245777 (denominator of (n/tau(n) - sigma(n)/n)) is at a(300); a(300) = 25, A245777(300) = 75. Sequence of numbers n such that A245777(n) is not equal to a(n): 300, 768, 1452, 1764, 2100, 3468, 3900, 5376, 5700, 6084, 6348, 9075, 9300, ... See (MAGMA) [n: n in [1..10000] | (Denominator((n/(#[d: d in Divisors(n)]))+(SumOfDivisors(n)/n))) - (Denominator((n/(#[d: d in Divisors(n)]))-(SumOfDivisors(n)/n))) ne 0]

LINKS

Jaroslav Krizek, <a href="/A245785/b245785.txt">Table of n, a(n) for n = 1..10000</a>

EXAMPLE

For n = 9; a(9) = denominator(9/tau(9) + sigma(9)/9) = denominator(9/3 + 13/9) = denominator(40/9) = 9.

PROG

(MAGMA) [Denominator((n/(#[d: d in Divisors(n)]))+(SumOfDivisors(n)/n)): n in [1..1000]]

CROSSREFS

Cf. A000005, A000203, A245784, A245786.

KEYWORD

allocated

nonn

AUTHOR

Jaroslav Krizek, Aug 15 2014

STATUS

approved

editing

#1 by Jaroslav Krizek at Fri Aug 01 10:42:29 EDT 2014

NAME

allocated for Jaroslav Krizek

KEYWORD

allocated

STATUS

approved