1,1

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

Walter Nissen, Abundancy : Some Resources

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 [From Gerard P. Michon (g.michon(AT)att.net), Jul 01 2009]

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.

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).

Sequence in context: A095480 A121977 A095482 this_sequence A095484 A095486 A095488

Adjacent sequences: A160675 A160676 A160677 this_sequence A160679 A160680 A160681

fini,nonn,bref

Gerard P. Michon (g.michon(AT)att.net), Jun 06 2009