A145338 a(n) is the smallest prime p where |d(p-1) - d(p+1)| = n. (d(m) = the number of divisors of m.)

7, 2, 11, 197, 23, 37, 47, 401, 59, 1601, 181, 16901, 167, 3137, 179, 577, 419, 1297, 1051, 12101, 359, 739601, 1009, 4357, 1511, 50177, 719, 171610001, 839, 67601, 10657, 9096257, 1439, 240101, 3697, 145540097, 3023, 15877, 2879, 3587237, 2521

Offset: 0

Author

Leroy Quet, Oct 08 2008

Keywords

• nonn

Comments

a(2n-1) = k^2 + 1, for all positive integers n, where k is some integer; k is even for n >= 2.

Examples

			a(2)=11 because abs(d(10) - d(12)) = 2 while abs(d(p-1) - d(p+1)) < 2 for p=2,3,5 and 7. - _Emeric Deutsch_, Oct 11 2008
		

Crossrefs

Cf. A145337.

Programs

Maple

with(numtheory); a:=proc(n) local j: for j while abs(tau(ithprime(j)-1)-tau(ithprime(j)+1)) <> n do end do: ithprime(j) end proc: seq(a(n), n=0..26); # Emeric Deutsch, Oct 11 2008

Extensions

More terms from R. J. Mathar and Emeric Deutsch, Oct 10 2008

Extended from a(27) onwards by Ray Chandler, Oct 12 2008