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

%I A230542 #16 Apr 08 2020 09:44:17
%S A230542 8,9,18,24,25,32,36,40,45,49,50,56,63,64,75,81,88,90,96,98,99,100,104,
%T A230542 117,120,121,125,126,128,136,147,150,152,153,160,162,168,169,171,175,
%U A230542 180,184,192,196,198,200,207,224,225,232,234,242,243,245,248,250,252
%N A230542 Numbers that cannot be divided by their multiplicative projection (A000026).
%C A230542 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 A230542 Paolo P. Lava, <a href="/A230542/b230542.txt">Table of n, a(n) for n = 1..5000</a>
%e A230542 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 A230542 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 A230542 with(numtheory); P:=proc(q) local a,k,n;
%p A230542 for n from 1 to q do a:=ifactors(n)[2];  b:=mul(a[k][2]*a[k][1],k=1..nops(a));
%p A230542 if not type(n/b,integer) then print(n); fi; od; end: P(10^6);
%t A230542 selQ[n_] := !Divisible[n, Times @@ Flatten[FactorInteger[n]]];
%t A230542 Select[Range[1000], selQ] (* _Jean-François Alcover_, Apr 08 2020 *)
%o A230542 (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 A230542 Cf. A000026, A159836.
%K A230542 nonn
%O A230542 1,1
%A A230542 _Paolo P. Lava_, Oct 24 2013
%E A230542 Missing a(85) in b-file inserted by _Andrew Howroyd_, Feb 26 2018