A096014 a(n) = (smallest prime factor of n) * (least prime that is not a factor of n), with a(1)=2.

2, 6, 6, 6, 10, 10, 14, 6, 6, 6, 22, 10, 26, 6, 6, 6, 34, 10, 38, 6, 6, 6, 46, 10, 10, 6, 6, 6, 58, 14, 62, 6, 6, 6, 10, 10, 74, 6, 6, 6, 82, 10, 86, 6, 6, 6, 94, 10, 14, 6, 6, 6, 106, 10, 10, 6, 6, 6, 118, 14, 122, 6, 6, 6, 10, 10, 134, 6, 6, 6, 142, 10, 146, 6, 6, 6, 14, 10, 158, 6, 6, 6

Offset: 1

Author

Reinhard Zumkeller, Jun 15 2004

Keywords

• nonn
• look

Links

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

Crossrefs

Cf. A001747, A020639, A053669, A073582, A096015.

Programs

Maple

f:= proc(n) local p;
p:= 3;
if n::even then
  while type(n/p,integer) do p:= nextprime(p) od;
else
  while not type(n/p,integer) do p:= nextprime(p) od:
fi;
2*p;
end proc:
f(1):= 2:
map(f, [$1..100]); # Robert Israel, Jun 22 2018

Mathematica

PrimeFactors[n_] := Flatten[ Table[ #[[1]], {1} ] & /@ FactorInteger[n]]; f[1] = 2; f[n_] := Block[ {k = 1}, While[ Mod[ n, Prime[k]] == 0, k++ ]; Prime[k]PrimeFactors[n][[1]]]; Table[ f[n], {n, 83}] (* Robert G. Wilson v, Jun 15 2004 *)
spfn[n_]:=Module[{fi=FactorInteger[n][[;;,1]],k=2},While[MemberQ[fi,k],k=NextPrime[k]];fi[[1]]*k]; Array[spfn,90] (* Harvey P. Dale, Sep 22 2024 *)

PARI

dnd(n) = forprime(p=2, , if (n % p, return(p)));
lpf(n) = if (n==1, 1, forprime(p=2, , if (!(n % p), return(p))));
a(n) = dnd(n)*lpf(n); \\ Michel Marcus, Jun 22 2018

Formula

a(n) = A020639(n)*A053669(n);

A096015(n) = a(n)/2.

If n (mod 6) = 2, 3 or 4, then a(n) = 6. If n (mod 6) = 0, 1 or 5, then a(n) belongs to A001747 less the first three terms or belongs to A073582 less the first two terms. - Robert G. Wilson v, Jun 15 2004

From Bill McEachen, Jul 26 2024: (Start)

a(n) <= 2*n, except when n = 2.

a(n) = 2*n for n an odd prime. (End)