A109766 Admirable numbers such that the subtracted divisor is prime.

12, 40, 70, 88, 1888, 4030, 5830, 8925, 32128, 32445, 78975, 442365, 521728, 1848964, 8378368, 34359083008, 66072609790

Offset

1,1

Comments

549753192448 is also a term. - Donovan Johnson, Sep 08 2012

Links

Table of n, a(n) for n=1..17.

Example

a(2) = 40 because 1+2+4+8+10+20-5 = 40 and the subtracted divisor is prime.

Mathematica

q[n_] := (ab = DivisorSigma[1, n] - 2 n) > 0 && EvenQ[ab] && ab/2 < n && Divisible[n, ab/2] && PrimeQ[ab/2]; Select[Range[2*10^6], q] (* Amiram Eldar, Aug 05 2023 *)

Crossrefs

Cf. A111592.

Sequence in context: A363121 A353839 A175583 * A365446 A033586 A211786

Adjacent sequences: A109763 A109764 A109765 * A109767 A109768 A109769

Keyword

nonn,more

Author

Jason Earls, Aug 13 2005

Extensions

a(15) from Donovan Johnson, Sep 27 2008

a(16)-a(17) from Donovan Johnson, Sep 08 2012

Status

approved