A230542 - OEIS

%I #16 Apr 08 2020 09:44:17

%S 8,9,18,24,25,32,36,40,45,49,50,56,63,64,75,81,88,90,96,98,99,100,104,

%T 117,120,121,125,126,128,136,147,150,152,153,160,162,168,169,171,175,

%U 180,184,192,196,198,200,207,224,225,232,234,242,243,245,248,250,252

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

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

%H Paolo P. Lava, <a href="/A230542/b230542.txt">Table of n, a(n) for n = 1..5000</a>

%e 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.

%e 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.

%p with(numtheory); P:=proc(q) local a,k,n;

%p for n from 1 to q do a:=ifactors(n)[2];  b:=mul(a[k][2]*a[k][1],k=1..nops(a));

%p if not type(n/b,integer) then print(n); fi; od; end: P(10^6);

%t selQ[n_] := !Divisible[n, Times @@ Flatten[FactorInteger[n]]];

%t Select[Range[1000], selQ] (* _Jean-François Alcover_, Apr 08 2020 *)

%o (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

%Y Cf. A000026, A159836.

%K nonn

%O 1,1

%A _Paolo P. Lava_, Oct 24 2013

%E Missing a(85) in b-file inserted by _Andrew Howroyd_, Feb 26 2018