A245778 Numbers n such that k(n) = n/tau(n) - sigma(n)/n is an integer.

1, 672, 4680, 30240, 435708, 23569920, 45532800, 4138364160, 14182439040, 53798734080, 153003540480, 403031236608, 518666803200

Offset

1,2

Comments

Numbers n such that A245776(n) / A245777(n) = (n / A000005(n) - A000203(n) / n) is an integer.

Sequence of integers k(n): 0, 25, 94, 311, 4031, 73652, 118571, …

Conjecture: subsequence of A216793.

Refactorable multiply-perfect numbers (A245782) are members of this sequence.

a(14) > 10^13. - Giovanni Resta, Jul 13 2015

The numbers 13661860101120 and 740344994887680 are also terms. - Giovanni Resta, Nov 14 2019

Links

Table of n, a(n) for n=1..13.

Formula

A245777(a(n)) = 1.

Example

672 is in sequence because 672 / tau(672) - sigma(672) / 672 = 672 / 24 - 2016 / 672 = 25 (integer).

Maple

select(n -> type(n/numtheory:-tau(n) - numtheory:-sigma(n)/n, integer), [$1..10^8]); # Robert Israel, Aug 03 2014

Prog

(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 01 2014

Crossrefs

Cf. A000005, A000203, A216793, A245776, A245777, A245779, A245782.

Sequence in context: A057797 A057802 A231740 * A245786 A321116 A234481

Adjacent sequences: A245775 A245776 A245777 * A245779 A245780 A245781

Keyword

nonn,more

Author

Jaroslav Krizek, Aug 01 2014

Extensions

a(8)-a(13) from Giovanni Resta, Jul 13 2015

Status

approved