login
A230542
Numbers that cannot be divided by their multiplicative projection (A000026).
2
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
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
Sequence in context: A095191 A050706 A159836 * A069809 A374118 A067544
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