A372009 -id:A372009 - cp's OEIS frontend

A372028 Numbers k such that A124652(k) divides A372111(k-1).

3, 5, 7, 11, 12, 13, 15, 16, 17, 18, 20, 22, 24, 26, 27, 28, 29, 30, 31, 33, 40, 41, 42, 43, 44, 46, 49, 50, 51, 53, 55, 58, 59, 60, 62, 63, 64, 66, 67, 68, 69, 70, 71, 72, 73, 78, 79, 80, 92, 93, 95, 98, 101, 102, 103, 104, 105, 107, 109, 111, 112, 115, 116, 117

Offset: 1

Michael De Vlieger, May 05 2024

nonn

Contains A372009(m), m > 1.

For k in this sequence, A124652(k) has the same relationship with A372111(k-1) as A109890(i) has with A109735(i-1) for i > 2.

			Let b(x) = A124652(x) and s(x) = A372111(x), where A372111 contains partial sums of A124652.
a(1) = 3 since b(3) = 3, a divisor of s(2) = 3.
a(2) = 5 since b(5) = 5, a divisor of s(4) = 10.
a(3) = 7 since b(7) = 6, a divisor of s(6) = 24, etc.

Michael De Vlieger, Table of n, a(n) for n = 1..10000
Michael De Vlieger, Log log scatterplot of A124652(n), n = 1..10^5, showing A124652(a(n)) in green, but A124652(a(n)) that are prime in red.

Cf. A007947, A027750, A109735, A109890, A124652, A372009, A372111, A372399.

nn = 120; 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];
Reap[Do[r = f[s]; k = SelectFirst[r, ! c[#] &];
  If[Divisible[s, k], Sow[i]]; c[k] = True;
  s += k, {i, 3, nn}] ][[-1, 1]]

A124652(a(n)) is a number in row A372111(a(n)-1) of A027750.

A372284 Primes in the order in which they appear in A124652.

Original entry on oeis.org

2, 3, 5, 11, 7, 31, 13, 19, 17, 37, 29, 41, 47, 59, 23, 97, 53, 829, 71, 149, 101, 167, 79, 151, 43, 103, 157, 113, 139, 109, 137, 197, 353, 89, 277, 293, 269, 229, 73, 61, 571, 83, 191, 691, 251, 179, 127, 257, 193, 173, 239, 163, 331, 613, 617, 311, 67, 523

Offset: 1

Michael De Vlieger, Apr 29 2024

nonn

Analogous to A111239, a sequence which instead pertains to A109890.

			Let b(x) = A372009(x).
Table of first terms:
   n  b(n) 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
  ...

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

Cf. A124652, A372009.

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[k]]; c[k] = True;
    s += k, {i, 3, nn}] ][[-1, 1]]

cp's OEIS Frontend

A372028 Numbers k such that A124652(k) divides A372111(k-1).

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

Formula