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

1,1

Links

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

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

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 *)

Prog

(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

Crossrefs

Cf. A020639, A053669, A096015.

Sequence in context: A048765 A103643 A079892 * A071888 A117217 A260930

Adjacent sequences: A096011 A096012 A096013 * A096015 A096016 A096017

Keyword

nonn,look

Author

Reinhard Zumkeller, Jun 15 2004

Status

approved