A372028 - OEIS

The OEIS is supported by the many generous donors to the OEIS Foundation.

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give

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