A372028 - OEIS

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

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

OFFSET

1,1

COMMENTS

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.

LINKS

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.

FORMULA

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

EXAMPLE

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.

MATHEMATICA

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]]

CROSSREFS

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

Sequence in context: A215464 A260910 A109908 * A152212 A347465 A249370

Adjacent sequences: A372025 A372026 A372027 * A372029 A372030 A372031

KEYWORD

nonn

AUTHOR

Michael De Vlieger, May 05 2024

STATUS

approved