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
Keywords
Examples
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.
Links
- Paolo P. Lava, Table of n, a(n) for n = 1..5000
Programs
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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);
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Mathematica
selQ[n_] := !Divisible[n, Times @@ Flatten[FactorInteger[n]]]; Select[Range[1000], selQ] (* Jean-François Alcover, Apr 08 2020 *)
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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
Extensions
Missing a(85) in b-file inserted by Andrew Howroyd, Feb 26 2018
Comments