A120635 Replace each prime power in the prime-factorization of n with the next higher prime-power.

1, 3, 4, 5, 7, 12, 8, 9, 11, 21, 13, 20, 16, 24, 28, 17, 19, 33, 23, 35, 32, 39, 25, 36, 27, 48, 29, 40, 31, 84, 32, 37, 52, 57, 56, 55, 41, 69, 64, 63, 43, 96, 47, 65, 77, 75, 49, 68, 53, 81, 76, 80, 59, 87, 91, 72, 92, 93, 61, 140, 64, 96, 88, 67, 112, 156, 71, 95, 100, 168, 73

Offset

1,2

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

12 = 2^2 *3^1. 5 is the prime power closest to 2^2 and larger than 2^2. 4 is the prime power closest to 3 and larger than 3. So a(12) = 5*4 = 20.

Maple

N:= 100: # for a(1)..a(N)
PP:= select(t -> nops(numtheory:-factorset(t))=1, [$2..N]):
g:= proc(n) local i;
   if member(n, PP, i) then PP[i+1] fi
  end proc:
f:= proc(n) local F;
  F:= ifactors(n)[2];
  convert(map(t -> g(t[1]^t[2]), F), `*`)
end proc:
map(f, [$1..N]); # Robert Israel, Mar 02 2022

Mathematica

nextPrimePower[n_] := Module[{k}, For[k = n+1, True, k++, If[PrimeNu[k] == 1, Return[k]]]];
a[n_] := If[n == 1, 1, Times @@ (nextPrimePower[Power @@ #]& /@ FactorInteger[n])];
Table[a[n], {n, 1, 100}] (* Jean-François Alcover, Feb 07 2023 *)

Prog

(PARI) { a(n) = local(f, r, k, d); f=factorint(n); r=1; for(i=1, matsize(f)[1], k=f[i, 1]^f[i, 2]+1; while(!isprime(k) && (!ispower(k, , &d)||!isprime(d)), k++); r*=k); r } \\ Max Alekseyev, Feb 01 2007

Crossrefs

Cf. A120636.

Sequence in context: A353969 A285224 A322991 * A300841 A023713 A032890

Adjacent sequences: A120632 A120633 A120634 * A120636 A120637 A120638

Keyword

nonn,mult

Author

Leroy Quet, Jun 22 2006

Extensions

More terms from Max Alekseyev, Feb 01 2007

Status

approved