A140222 A number j is included if (Sum_{k=1..j} d(k)) is prime, where d(k) is the number of divisors of k.

2, 3, 9, 11, 13, 14, 28, 29, 31, 34, 35, 51, 54, 56, 61, 81, 83, 93, 94, 97, 98, 123, 124, 131, 140, 142, 171, 173, 177, 179, 180, 185, 187, 190, 191, 193, 195, 228, 230, 231, 233, 234, 248, 251, 290, 293, 294, 296, 297, 304, 309, 310, 315, 316, 320, 322, 373

Offset

1,1

Comments

Sum_{k=1..j} d(k) = Sum_{k=1..j} floor(j/k) = A006218(j).

Links

Michael De Vlieger, Table of n, a(n) for n = 1..10000

Example

9 is in the sequence because the number of divisors of 1,2,...,9 are 1,2,2,3,2,4,2,4,3, respectively, having as sum the prime number 23.

Maple

with(numtheory): a:=proc(n) if isprime(sum(tau(k), k=1..n))=true then n else end if end proc: seq(a(n), n=1..400); # Emeric Deutsch, Jun 08 2008

Mathematica

Position[Accumulate@ DivisorSigma[0, Range@ 400], _?PrimeQ][[All, 1]] (* Michael De Vlieger, Feb 19 2019 *)

Crossrefs

Cf. A006218, A140221.

Sequence in context: A229492 A328970 A103039 * A272537 A121557 A138984

Adjacent sequences: A140219 A140220 A140221 * A140223 A140224 A140225

Keyword

nonn

Author

Leroy Quet, May 12 2008

Extensions

More terms from Emeric Deutsch, Jun 08 2008

Status

approved