A230542 Numbers that cannot be divided by their multiplicative projection (A000026).

8, 9, 18, 24, 25, 32, 36, 40, 45, 49, 50, 56, 63, 64, 75, 81, 88, 90, 96, 98, 99, 100, 104, 117, 120, 121, 125, 126, 128, 136, 147, 150, 152, 153, 160, 162, 168, 169, 171, 175, 180, 184, 192, 196, 198, 200, 207, 224, 225, 232, 234, 242, 243, 245, 248, 250, 252

Offset

1,1

Comments

Subset of A159836. For n < 1000 only 6 terms (144, 216, 256, 400, 576, 648, 720 and 768) are missing with respect to A159836.

Links

Paolo P. Lava, Table of n, a(n) for n = 1..5000

Example

Prime factors of 88 are 2^3 and 11; its multiplicative projection is 2*3*11 = 66 and 66 does not divide 88. Therefore 88 is in the sequence.
Prime factors of 108 are 2^2 and 3^3; its multiplicative projection is 2*2*3*3 = 36 and 108 / 36 = 3. therefore 108 is not in the sequence.

Maple

with(numtheory); P:=proc(q) local a, k, n;
for n from 1 to q do a:=ifactors(n)[2];  b:=mul(a[k][2]*a[k][1], k=1..nops(a));
if not type(n/b, integer) then print(n); fi; od; end: P(10^6);

Mathematica

selQ[n_] := !Divisible[n, Times @@ Flatten[FactorInteger[n]]];
Select[Range[1000], selQ] (* Jean-François Alcover, Apr 08 2020 *)

Prog

(PARI) ok(n)={my(f=factor(n)); n % prod(k=1, matsize(f)[1], f[k, 1]*f[k, 2]) <> 0} \\ Andrew Howroyd, Feb 26 2018

Crossrefs

Cf. A000026, A159836.

Sequence in context: A095191 A050706 A159836 * A069809 A374118 A067544

Adjacent sequences: A230539 A230540 A230541 * A230543 A230544 A230545

Keyword

nonn

Author

Paolo P. Lava, Oct 24 2013

Extensions

Missing a(85) in b-file inserted by Andrew Howroyd, Feb 26 2018

Status

approved