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

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

Offset: 1

Author

Jaroslav Krizek, Aug 15 2014

Keywords

• nonn

Comments

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

Examples

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

Crossrefs

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

Programs

Magma

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

PARI

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

Formula

A245785(a(n)) = 1.

Extensions

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