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A090482
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Smallest prime p such that tau(p-1) + tau(p+1) is n, or 0 if no such number exists.
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4
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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; internal format)
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OFFSET
| 1,3
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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 (wasserma(AT)spawar.navy.mil), Nov 17 2005
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FORMULA
| Least prime p such that A175144(p) = n.
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EXAMPLE
| a(10) = 11, tau(10) = 4 and tau(12) = 6, 4+6=10.
a(16) = 41, a(17) = 101.
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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 *)
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CROSSREFS
| Cf. A090481, A090483, A175144.
Sequence in context: A011013 A138325 A117175 * A082857 A081155 A130628
Adjacent sequences: A090479 A090480 A090481 * A090483 A090484 A090485
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KEYWORD
| nonn
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AUTHOR
| Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Dec 02 2003
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EXTENSIONS
| More terms from David Wasserman (wasserma(AT)spawar.navy.mil), Nov 17 2005
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