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

Author

Jason Earls, Aug 13 2005

Keywords

• nonn
• more

Comments

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

Examples

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

Crossrefs

Cf. A111592.

Programs

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 *)

Extensions

a(15) from Donovan Johnson, Sep 27 2008

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