A066260 In the prime factorization of n replace the k-th prime with the k-th composite number, k > 0.
1, 4, 6, 16, 8, 24, 9, 64, 36, 32, 10, 96, 12, 36, 48, 256, 14, 144, 15, 128, 54, 40, 16, 384, 64, 48, 216, 144, 18, 192, 20, 1024, 60, 56, 72, 576, 21, 60, 72, 512, 22, 216, 24, 160, 288, 64, 25, 1536, 81, 256, 84, 192, 26, 864, 80, 576, 90, 72, 27, 768, 28, 80, 324
Offset: 1
Examples
a(10) = a(2*5) = a(prime(1)*prime(3)) = a(prime(1))*a(prime(3)) = comp(1)*comp(3) = 4 * 8 = 32.
Links
- Harry J. Smith, Table of n, a(n) for n = 1..1000
- Index to divisibility sequences
Programs
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Maple
b:= proc(n) option remember; local k; if n=1 then 4 else for k from 1+b(n-1) while isprime(k) do od; k fi end: a:= n-> mul(b(numtheory[pi](i[1]))^i[2], i=ifactors(n)[2]): seq(a(n), n=1..63); # Alois P. Heinz, Mar 21 2025 -
Mathematica
nmax = 100; compos = Select[Range[FindRoot[n == nmax + PrimePi[n] + 1, {n, nmax, 2 nmax}][[1, 2]] // Floor], CompositeQ]; a[n_] := If[n == 1, 1, Product[{p, e} = pe; compos[[PrimePi[p]]]^e, {pe, FactorInteger[n]}]]; Array[a, nmax] (* Jean-François Alcover, Nov 21 2021 *) -
PARI
Composite(n) = local(k); k=n + primepi(n) + 1; while (k != n + primepi(k) + 1, k = n + primepi(k) + 1); return(k) for (n=1, 1000, f=factor(n); a=1; for (i=1, matsize(f)[1], a*=Composite(primepi(f[i, 1]))^f[i, 2]); write("b066260.txt", n, " ", a) ) \\ Harry J. Smith, Feb 07 2010