A066260 -id:A066260 - cp's OEIS frontend

A066261 a(n) = A066260(A066260(n)).

1, 16, 24, 256, 64, 384, 36, 4096, 576, 1024, 32, 6144, 96, 576, 1536, 65536, 36, 9216, 48, 16384, 864, 512, 256, 98304, 4096, 1536, 13824, 9216, 144, 24576, 128, 1048576, 768, 576, 2304, 147456, 54, 768, 2304, 262144, 40, 13824, 384, 8192, 36864, 4096

Offset: 1

Reinhard Zumkeller, Dec 10 2001

Completely multiplicative since A066260 is (iterates of completely multiplicative functions are too). - David W. Wilson, Jun 09 2005

Harry J. Smith, Table of n, a(n) for n = 1..1000
Index to divisibility sequences

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]); f=factor(a); a=1; for (i=1, matsize(f)[1], a*=Composite(primepi(f[i, 1]))^f[i, 2]); write("b066261.txt", n, " ", a) ) \\ Harry J. Smith, Feb 07 2010

A066262 a(n) = gcd(n, A066260(n)).

Original entry on oeis.org

1, 2, 3, 4, 1, 6, 1, 8, 9, 2, 1, 12, 1, 2, 3, 16, 1, 18, 1, 4, 3, 2, 1, 24, 1, 2, 27, 4, 1, 6, 1, 32, 3, 2, 1, 36, 1, 2, 3, 8, 1, 6, 1, 4, 9, 2, 1, 48, 1, 2, 3, 4, 1, 54, 5, 8, 3, 2, 1, 12, 1, 2, 9, 64, 1, 6, 1, 4, 3, 2, 1, 72, 1, 2, 3, 4, 1, 6, 1, 16, 81, 2, 1, 12, 1, 2, 3, 8, 1, 18, 1, 4, 3, 2, 5, 96

Offset: 1

Reinhard Zumkeller, Dec 10 2001

nonn

Same as A065331 through a(54); A065331(55)=1, but a(55)=5. - Jon E. Schoenfield, Jan 28 2022

Harry J. Smith, Table of n, a(n) for n = 1..1000

Cf. A066260.

Different from A065331.

Composite(n) = { my(k=n + primepi(n) + 1); while (k != n + primepi(k) + 1, k = n + primepi(k) + 1); return(k) }
{ for (n=1, 100, my(f=factor(n), a=1); for (i=1, matsize(f)[1], a*=Composite(primepi(f[i, 1]))^f[i, 2]); a=gcd(n, a); print1(a, ", ") ) } \\ Harry J. Smith, Feb 07 2010

A382265 In the prime factorization of n replace the k-th prime with the k-th nonprime number.

Original entry on oeis.org

1, 1, 4, 1, 6, 4, 8, 1, 16, 6, 9, 4, 10, 8, 24, 1, 12, 16, 14, 6, 32, 9, 15, 4, 36, 10, 64, 8, 16, 24, 18, 1, 36, 12, 48, 16, 20, 14, 40, 6, 21, 32, 22, 9, 96, 15, 24, 4, 64, 36, 48, 10, 25, 64, 54, 8, 56, 16, 26, 24, 27, 18, 128, 1, 60, 36, 28, 12, 60, 48, 30, 16, 32, 20, 144

Offset: 1

Ilya Gutkovskiy, Mar 19 2025

Alois P. Heinz, Table of n, a(n) for n = 1..10000

Cf. A000720, A003963, A018252, A066260.

b:= proc(n) option remember; local k; if n=1 then 1 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..75);  # Alois P. Heinz, Mar 21 2025

nonPrime[n_] := FixedPoint[n + PrimePi@# &, n + PrimePi@ n]; (* Robert G. Wilson v at A018252 *)
non[p_] := non[p] = nonPrime[PrimePi[p]]; f[p_, e_] := non[p]^e; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Mar 21 2025 *)

If n = Product prime(k)^e(k) then a(n) = Product nonprime(k)^e(k).

cp's OEIS Frontend

A066261 a(n) = A066260(A066260(n)).

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A066262 a(n) = gcd(n, A066260(n)).

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A382265 In the prime factorization of n replace the k-th prime with the k-th nonprime number.

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