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

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

1,3

Links

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

Formula

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

Maple

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

Mathematica

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 *)

Crossrefs

Cf. A000720, A003963, A018252, A066260.

Sequence in context: A000593 A115607 A318876 * A330356 A329428 A288469

Adjacent sequences: A382262 A382263 A382264 * A382266 A382267 A382268

Keyword

nonn,mult

Author

Ilya Gutkovskiy, Mar 19 2025

Status

approved