A160678 Numbers n whose abundancy is equal to 13/2; sigma(n)/n = 13/2.

170974031122008628879954060917200710847692800, 1893010442758976546037991125738431754692198400, 54361481238923605327597493185154939181072384000

Offset: 1

Author

Gerard P. Michon, Jun 06 2009

Keywords

• nonn

Comments

This sequence includes many terms but it is conjectured to be finite.

Examples

			a(1) = 2^23 3^9 5^2 7^5 11^5 13^2 17 19^3 31 37 43 61^2 97 181 241.
As the "sum of divisors" function (sigma) is a multiplicative function, sigma(a(1)) is the product of the values of sigma at the above prime powers, respectively given as follows, in factorized form:
sigma(a(1)) = (3^2 5 7 13 17 241) (2^2 11^2 61) (31) (2^3 3 19 43) (2^2 3^2 7 19 37) (3 61) (2 3^2) (2^3 5 181) (2^5) (2 19) (2^2 11) (3 13 97) (2 7 13) (2 7^2) (2 11^2).
a(1) belongs to the sequence because the latter product boils down to 13/2 times the former.
		

Links

• Michel Marcus, Table of n, a(n) for n = 1..307
• G. P. Michon, Multiperfect and hemiperfect integers
• G. P. Michon, Multiplicative functions: Abundancy = sigma(n)/n
• G. P. Michon and M. Marcus, Hemiperfect numbers of abundancy 13/2
• Walter Nissen, Abundancy: Some Resources

Crossrefs

Cf. A000203 (sigma function, sum of divisors), A141643 (abundancy = 5/2), A055153 (abundancy = 7/2), A141645 (abundancy = 9/2), A159271 (abundancy = 11/2), A159907 (half-integral abundancy, "hemiperfect numbers"), A088912 (least numbers of given half-integer abundancy). A007691 (multiperfect numbers, abundancy is an integer), A000396 (perfect numbers, abundancy = 2), A005101 (abundant numbers, abundancy is greater than 2), A005100 (deficient numbers, abundancy is less than 2).

Programs

PARI

is(n)=sigma(n,-1)==13/2 \\ Charles R Greathouse IV, Feb 21 2017