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

1,3

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

Links

Table of n, a(n) for n=1..52.

Formula

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

Example

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

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 *)

Crossrefs

Cf. A090481, A090483, A175144.

Sequence in context: A258323 A117175 A228086 * A082857 A208092 A081155

Adjacent sequences: A090479 A090480 A090481 * A090483 A090484 A090485

Keyword

nonn

Author

Amarnath Murthy, Dec 02 2003

Extensions

More terms from David Wasserman, Nov 17 2005

Status

approved