A245785 -id:A245785 - cp's OEIS frontend

A245777 Denominator of (n / tau(n) - sigma(n) / n).

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

Jaroslav Krizek, Aug 01 2014

Denominator of (n / A000005(n) - A000203(n) / n).
See A245776 - numerator of (n / tau(n) - sigma(n) / n).
If n is an odd prime, a(n) = 2*n. - Robert Israel, Aug 01 2014
First deviation from A245785 (denominator of (n/tau(n) +  sigma(n)/n)) is at a(300); a(300) = 75, A245785(300) = 25. Sequence of numbers n such that A245785(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] - Jaroslav Krizek, Aug 15 2014

			For n = 9; a(9) = denominator(9/tau(9) - sigma(9)/9) = denominator(9/3 - 13/9) = denominator(14/9) = 9.

Michael De Vlieger, Table of n, a(n) for n = 1..10000

Cf. A000005, A000203, A245776, A245778, A245779, A245782.

[Denominator((n/(#[d: d in Divisors(n)]))-(SumOfDivisors(n)/n)): n in [1..100]]

Table[Denominator[n/DivisorSigma[0, n] - DivisorSigma[1, n]/n], {n, 70}] (* Alonso del Arte, Aug 15 2014 *)

vector(150, n, denominator(n/numdiv(n) - sigma(n)/n)) \\ Derek Orr, Aug 01 2014

A245776(n) / a(n) < 1 for numbers n in A245779.
A245776(n) / a(n) = integer for numbers n in A245778.
a(n) = 1 for numbers n in A245778.

A245784 Numerator of (n/tau(n) + sigma(n)/n).

Original entry on oeis.org

2, 5, 17, 37, 37, 7, 65, 31, 40, 43, 145, 13, 197, 73, 107, 411, 325, 31, 401, 163, 569, 157, 577, 11, 718, 211, 889, 20, 901, 123, 1025, 701, 427, 343, 1417, 235, 1445, 421, 1745, 29, 1765, 211, 1937, 305, 277, 601, 2305, 443, 2572, 1529, 963, 823, 2917, 323

Offset: 1

Jaroslav Krizek, Aug 15 2014

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

See A245785 - denominator of (n/tau(n) + sigma(n)/n).

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

Jaroslav Krizek, Table of n, a(n) for n = 1..10000

Cf. A000005, A000203, A245785, A245786.

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

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

A245786 Numbers n such that k(n) = (n/tau(n) + sigma(n)/n) is an integer.

Original entry on oeis.org

1, 672, 4680, 30240, 23569920, 45532800, 275890944, 14182439040, 153003540480, 403031236608, 518666803200

Offset: 1

Jaroslav Krizek, Aug 15 2014

nonn

Numbers n such that A245784(n) / A245785(n) =  (n / A000005(n) + A000203(n) / n) is an integer.
Sequence of numbers k(n): 2, 31, 101, 319, 73660, 118579, …
Conjecture: Subsequence of A216793.
Refactorable multiply-perfect numbers (A245782) are members of this sequence.
a(12) > 10^13. - Giovanni Resta, Jul 13 2015

			672 is in sequence because 672/tau(672) + sigma(672)/672 = 672/24 + 2016/672 = 31 (integer).

Cf. A000005, A000203, A245784, A245785, A245782.

[n: n in [1..100000] | (Denominator((n/(#[d: d in Divisors(n)])) + (SumOfDivisors(n)/n)) eq 1)]

for(n=1, 10^8, s=n/numdiv(n); t=sigma(n)/n; if(floor(s+t)==s+t, print1(n, ", "))) \\ Derek Orr, Aug 15 2014

A245785(a(n)) = 1.

a(7)-a(11) from Giovanni Resta, Jul 13 2015

cp's OEIS Frontend

A245777 Denominator of (n / tau(n) - sigma(n) / n).

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Magma

Mathematica

PARI

Formula

A245784 Numerator of (n/tau(n) + sigma(n)/n).

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Magma

PARI

A245786 Numbers n such that k(n) = (n/tau(n) + sigma(n)/n) is an integer.

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

Magma

PARI

Formula

Extensions