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A090482 Smallest prime p such that tau(p-1) + tau(p+1) is n, or 0 if no such number exists. 4
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified December 5 04:13 EST 2020. Contains 338943 sequences. (Running on oeis4.)