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
Keywords
Examples
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.
Links
- Michael De Vlieger, Table of n, a(n) for n = 1..10000
Programs
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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
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Mathematica
Position[Accumulate@ DivisorSigma[0, Range@ 400], ?PrimeQ][[All, 1]] (* _Michael De Vlieger, Feb 19 2019 *)
Extensions
More terms from Emeric Deutsch, Jun 08 2008
Comments