A181053 Numbers n such that Sum_{k=1..n} (-1)^(n-k) *tau(k) is prime.

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

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