A239578 Smallest number m such that the numerator of sigma(m)/m is equal to n, or zero if no such m exists.

1, 6, 2, 3, 24, 5, 4, 7, 10, 1080, 35640, 11, 9, 13, 8, 33, 297600, 17, 588, 19, 20, 1782, 1907020800, 23, 216, 45, 34, 78

Offset: 1

Author

Michel Marcus, Mar 21 2014

Keywords

• nonn
• more

Comments

If n-1 is prime, a(n) = n-1.

a(29) <= 1176249221876579007725568000.

Index of first occurrence of n in A017665. - Michel Marcus, Mar 24 2014

Examples

			a(2) = 6 since 6 is the first perfect number, with 2 as the numerator of sigma(6)/6.
a(3) = 2 because sigma(2)/2 = 3/2 and it is the first number that gives this numerator.
		

Links

• Giovanni Resta, Terms a(n) < 10^12, for n <= 1000

Crossrefs

Cf. A017665 (numerator of sigma(n)/n), A162657 (similar sequence but related to denominators).

Programs

PARI

a(n) = {k = 1; while (numerator(sigma(k)/k) != n, k++); k;}

Extensions

a(23) = 1907020800 confirmed by Giovanni Resta, Mar 21 2014