A090482 Smallest prime p such that tau(p-1) + tau(p+1) is n, or 0 if no such number exists.

0, 0, 2, 0, 3, 0, 5, 7, 0, 11, 17, 19, 37, 29, 0, 41, 101, 79, 0, 71, 197, 179, 401, 199, 2917, 181, 577, 239, 3137, 883, 4357, 419, 1297, 701, 12101, 839, 62501, 881, 30977, 1429, 21317, 2351, 16901, 1259, 287297, 1871, 1008017, 2161, 7057, 4049, 215297, 3079

Offset: 1

Author

Amarnath Murthy, Dec 02 2003

Keywords

• nonn

Comments

a(9)=0. Proof: Both p-1 and p+1 are even and composite hence 9=1+8 and 9=2+7 are ruled out, the only possibilities that remain are 9 = 3+6, or 9=4+5. 3+6 is ruled out as 4 is the only even number with 3 divisors. 4+5 is ruled out as 16 is the only even number with 5 divisors.

a(15) = a(19) = 0 is also provable. - David Wasserman, Nov 17 2005

Examples

			a(10) = 11, tau(10) = 4 and tau(12) = 6, 4+6=10.
a(16) = 41, a(17) = 101.
		

Crossrefs

Cf. A090481, A090483, A175144.

Programs

Mathematica

nn = 60; t = Table[-1, {nn}]; t[[{1,2,4,6,9,15,19}]] = 0; cnt = 7; p = 1; While[cnt < nn, p = NextPrime[p]; s = DivisorSigma[0, p-1] + DivisorSigma[0, p+1]; If[s <= nn && t[[s]] == -1, t[[s]] = p; cnt++]]; t (* T. D. Noe, Apr 28 2011 *)

Formula

Least prime p such that A175144(p) = n.

Extensions

More terms from David Wasserman, Nov 17 2005