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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
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified August 8 23:02 EDT 2020. Contains 336300 sequences. (Running on oeis4.)