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

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

Offset: 1

Author

T. D. Noe, May 09 2012

Keywords

• nonn
• hard
• more

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

Examples

			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.
		

Links

• 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

Crossrefs

Cf. A000203 (sigma), A050973, A211679.

Extensions

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

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