A181054 Numbers n such that Sum_{k=1..n} (-1)^(n-k)*sigma(k) is prime.

2, 3, 4, 6, 10, 22, 24, 32, 64, 66, 68, 92, 102, 112, 134, 168, 240, 262, 264, 270, 274, 316, 396, 442, 448, 538, 540, 542, 554, 560, 562, 582, 608, 612, 650, 652, 654, 668, 672, 786, 788, 866, 880, 924, 938, 940, 942, 948, 984, 988, 1008, 1018, 1064, 1074

Offset: 1

Author

Michel Lagneau, Oct 01 2010

Keywords

• nonn

Comments

These are the positions of primes in (-1)^(n-1)*A068762(n) = 1, 2, 2, 5, 1, 11, -3, 18, -5, 23, ... [R. J. Mathar, Nov 18 2010]

The first primes generated by the alternating sum are 2, 2, 5, 11, 23, 103, 139, 239, 859, 919, 977, 1811, 2207, 2657, ...

Examples

			4 is in the sequence because Sum_{k=1..4} (-1)^(4-k)*sigma(k) = (-1)^3*1 + (-1)^2*3 + (-1)^1*4 + (-1)^0*7 = -1 + 3 - 4 + 7 = 5 is prime.
		

Crossrefs

Cf. A000203, A068762.

Programs

Maple

with(numtheory): for n from 1 to 2000 do:x:=sum((((-1)^(n-k))*sigma(k),k=1..n)): if type(x,prime)=true then printf(`%d, `, n):else fi:od:

PARI

isok(n) = isprime(sum(k=1, n, (-1)^(n-k)*sigma(k))); \\ Michel Marcus, Oct 04 2017