A211677 First number k whose value of sigma(k)/k appears n times.

1, 28, 496, 1638, 24384, 2886100, 13035330, 29410290, 4426793280

Offset

1,2

Comments

The values of sigma(k)/k are 1, 2, 2, 8/3, 8/3, 96/35, 32/9, 32/9, 32/7. Note that these values are nondecreasing. Is that always the case? In the table below, all numbers in the same row are friendly to each other.

a(10) <= 27477725184. a(11) <= 88071903612. a(12) <= A027687(12). - Donovan Johnson, Aug 06 2012

For n>1, these are the smallest numbers to appear consecutively (n-1) times in A050973. - Michel Marcus, Jan 28 2014

Links

Table of n, a(n) for n=1..9.

Claude W. Anderson and Dean Hickerson, Problem 6020: Friendly Integers, Amer. Math. Monthly 84 (1977) pp. 65-66.

Achim Flammenkamp, Multiply Perfect Numbers (sigma(k)/k is an integer)

Tom De Medts, MathOverflow: Recovering n from sigma(n)/n

Carl Pomerance, Multiply perfect numbers, Mersenne primes and effective computability, Math. Ann. 226 (1977), 195-206.

Eric W. Weisstein, Friendly number

Eric W. Weisstein, Friendly pair

Wikipedia, Friendly number

Example

These are the values of k such that sigma(k)/k appears n times:
n   k values
1:  1
2:  6, 28
3:  6, 28, 496
4:  84, 270, 1488, 1638
5:  84, 270, 1488, 1638, 24384
6:  210, 17360, 43400, 284480, 2229500, 2886100
7:  3780, 66960, 167400, 406224, 1097280, 6656832, 13035330
8:  3780, 66960, 167400, 406224, 1097280, 6656832, 13035330, 29410290
9:  164989440, 270138960, 318729600, 326781000, 481572000, 623397600, 675347400, 995248800, 4426793280 - Donovan Johnson, Aug 06 2012
These numbers appear in A211679.

Crossrefs

Cf. A000203 (sigma), A050973, A211679.

Sequence in context: A240463 A140107 A028170 * A076172 A004336 A079598

Adjacent sequences: A211674 A211675 A211676 * A211678 A211679 A211680

Keyword

nonn,hard,more

Author

T. D. Noe, May 09 2012

Extensions

a(7)-a(8) from Donovan Johnson, May 10 2012

a(9) from Michel Marcus and Donovan Johnson, Aug 06 2012

Status

approved