A372009 Indices k such that A124652(k) is prime.

2, 3, 5, 11, 12, 20, 24, 28, 29, 33, 42, 43, 53, 58, 67, 78, 93, 98, 104, 105, 109, 112, 118, 125, 126, 137, 141, 145, 146, 162, 174, 182, 185, 187, 188, 195, 200, 223, 224, 231, 232, 239, 246, 249, 252, 255, 259, 264, 271, 275, 283, 286, 287, 296, 298, 300, 326

Offset

1,1

Comments

Analogous to A111238, a sequence which instead pertains to A109890.

Links

Michael De Vlieger, Table of n, a(n) for n = 1..2500

Michael De Vlieger, Log log scatterplot of A124652(n), n = 1..25000, showing primes in red.

Formula

Proper subset of A372028.

Example

Let b(x) = A124652(x).
Table of first terms.
   n  a(n)  b(a(n))
  -----------------
   1    2      2
   2    3      3
   3    5      5
   4   11     11
   5   12      7
   6   20     31
   7   24     13
   8   28     19
   9   29     17
  10   33     37
  11   42     29
  12   43     41
  ...

Mathematica

nn = 300; c[_] := False;
rad[x_] := rad[x] = Times @@ FactorInteger[x][[All, 1]];
f[x_] := Select[Range[x], Divisible[x, rad[#]] &];
Array[Set[{a[#], c[#]}, {#, True}] &, 2]; s = a[1] + a[2];
{2}~Join~Reap[Do[r = f[s]; k = SelectFirst[r, ! c[#] &];
    If[PrimeQ[k], Sow[i]]; c[k] = True;
    s += k, {i, 3, nn}] ][[-1, 1]]

Crossrefs

Cf. A124652, A372028, A372284.

Sequence in context: A243357 A066159 A316794 * A103027 A093902 A269004

Adjacent sequences: A372006 A372007 A372008 * A372010 A372011 A372012

Keyword

nonn,new

Author

Michael De Vlieger, Apr 29 2024

Status

approved