A376834 - OEIS

A376834

Numbers k that have at least 1 powerful number m such that 1 < m <= k that are not prime powers such that rad(m) | k, where rad = A007947.

36, 42, 48, 54, 60, 66, 72, 78, 84, 90, 96, 100, 102, 108, 110, 114, 120, 126, 130, 132, 138, 140, 144, 150, 156, 160, 162, 168, 170, 174, 180, 186, 190, 192, 196, 198, 200, 204, 210, 216, 220, 222, 224, 225, 228, 230, 234, 238, 240, 246, 250, 252, 255, 258, 260

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

OFFSET

1,1

COMMENTS

Numbers k such that A286708 and row k of A162306 meet.

Contains A286708, since for k in A286708, m = k is such that rad(m) | k.

LINKS

Michael De Vlieger, Table of n, a(n) for n = 1..10000

Michael De Vlieger, Plot p^e | a(n) at (x,y) = (n,pi(p)), n = 1..1500, pi = A000720, with a color function indicating exponent e = 1 in black, e = 2 = red, e = 3 = orange, ..., maximum e in magenta. The indicator bar below the image represents squarefree a(n) in green, a(n) in A332785 in blue, and a(n) in A286708 in violet.

EXAMPLE

Table showing select values of a(n):

n a(n) A286708 Intersect row a(n) of A162306.

---------------------------------------------------------------

1 36 = 2^2 * 3^2 {36}

2 42 = 2 * 3 * 7 {36}

3 48 = 2^4 * 3 {36}

4 54 = 2 * 3^3 {36}

5 60 = 2^2 * 3 * 5 {36}

6 66 = 2 * 3 * 11 {36}

7 72 = 2^3 * 3^2 {36, 72}

8 78 = 2 * 3 * 13 {36, 72}

9 84 = 2^2 * 3 * 7 {36, 72}

14 108 = 2^2 * 3^3 {36, 72, 108}

17 120 = 2^3 * 3 * 5 {36, 72, 100, 108}

24 150 = 2 * 3 * 5^2 {36, 72, 100, 108, 144}

MATHEMATICA

rad[x_] := rad[x] = Times @@ FactorInteger[x][[All, 1]];

Reap[Do[m = 1; k = 0;

While[Nor[k == 2, m == n + 1],

If[And[Divisible[n, #], Divisible[m, #^2], ! PrimePowerQ[m] ] &[

rad[m]], k++]; m++];

If[k == 2, Sow[n]], {n, 2^10}] ][[-1, 1]]

CROSSREFS

Cf. A001694, A007947, A162306, A286708.

Sequence in context: A261258 A261372 A044862 * A162526 A078299 A225028

Adjacent sequences: A376830 A376831 A376833 * A376835 A376836 A376837

KEYWORD

nonn

AUTHOR

Michael De Vlieger, Oct 06 2024

STATUS

approved