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 A181053 Numbers n such that Sum_{k=1..n} (-1)^(n-k) *tau(k) is prime. 1
 4, 10, 12, 14, 26, 28, 30, 32, 34, 50, 52, 54, 56, 58, 82, 92, 94, 124, 130, 132, 134, 136, 138, 176, 178, 186, 234, 240, 292, 300, 302, 304, 306, 308, 312, 366, 372, 374, 376, 384, 390, 392, 394, 398, 458, 540, 548, 564, 566, 570, 632, 634, 638, 644, 646, 654 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The partial alternating sums of the number of divisors tau(.)=A000005(.) are 1, 1, 1, 2, 0, 4, -2, 6, -3, 7, -5, 11, -9, 13,.. for n>=0. The first primes generated are 2, 7, 11, 13, 29, 31, 37, 41, 41, 71, 73, 79, 83, 83, 131, 157, 157, 223,... for upper limits of the sum as recorded by the sequence. LINKS Amiram Eldar, Table of n, a(n) for n = 1..10000 EXAMPLE n=4 is in the sequence because sum_{k=1..4} (-1)^(4-k)*tau(k) = (-1)^3*1 + (-1)^2*2 + (-1)^1*2 + (-1)^0*3 = -1 +2 -2 + 3 = 2 is prime. MAPLE with(numtheory): for n from 1 to 1000 do: x:=sum((((-1)^(n-k))*tau(k), k=1..n)): if type(x, prime)=true then printf(`%d, `, n): fi: od: MATHEMATICA s={}; sum=0; Do[sum = DivisorSigma[0, n] - sum; If[sum > 0 && PrimeQ[sum], AppendTo[s, n]], {n, 1, 654}]; s (* Amiram Eldar, Sep 10 2019 *) CROSSREFS Cf. A000005. Sequence in context: A155475 A023693 A299634 * A239055 A295129 A287338 Adjacent sequences:  A181050 A181051 A181052 * A181054 A181055 A181056 KEYWORD nonn AUTHOR Michel Lagneau, Oct 01 2010 EXTENSIONS Comment slightly extended by R. J. Mathar, Oct 24 2010 STATUS approved

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Last modified October 23 22:36 EDT 2019. Contains 328377 sequences. (Running on oeis4.)