A190274 Numbers n such that n' = p^2-1, with n = semiprime = p*q, n' is the arithmetic derivative of n. Also: semiprimes of the form p*(p^2-p-1).

15, 95, 287, 1199, 4607, 23519, 28799, 101567, 223199, 296207, 352799, 903167, 1019999, 2032127, 2230799, 2666159, 3285599, 5896799, 7606367, 13939199, 19392479, 28839887, 36154799, 46139039, 54295919, 62412767, 68250239, 73384079, 74440799, 90316799, 95234687, 109672319, 115263647, 118129199, 214562399, 223279487, 234503807, 236792879, 262963199, 270420767, 309829727, 355897439, 422999999, 486823247, 589884959, 628687487

Offset: 1

Author

Giorgio Balzarotti, May 07 2011

Keywords

• nonn

Comments

The sequence shows similarity with the Rassias Conjecture ("for any prime p there are two primes p1 and p2 such that p*p1=p1+p2+1, p>2, p2>p1") with p1=p we have p*p=p+p2-1 (see A190272). Generalization can be achieved by removing semiprimarity condition and accepting p^e, e>=2.

Examples

			n=15, 15'=8, a=8+1=9=3^2 -> a(1)=15
		

Links

• European Mathematical Society, Newsletter (see book reviews), March 2011, page 46.

Crossrefs

Cf. A001358 (semiprime), A003415 (arithmetic derivative), A190273 (n'=a-1), A190273 (n'=a+1).

Programs

Maple

seq(`if`(isprime((ithprime(i)^2-ithprime(i)-1))=true,(ithprime(i)^2-ithprime(i)-1)*ithprime(i),NULL),i=1..300);