A079431 Least m>n with same smallest odd prime factor as n.

2, 4, 6, 8, 10, 9, 14, 16, 12, 20, 22, 15, 26, 28, 18, 32, 34, 21, 38, 25, 24, 44, 46, 27, 35, 52, 30, 49, 58, 33, 62, 64, 36, 68, 40, 39, 74, 76, 42, 50, 82, 45, 86, 88, 48, 92, 94, 51, 56, 55, 54, 104, 106, 57, 65, 77, 60, 116, 118, 63, 122, 124, 66, 128, 70, 69, 134, 136

Offset: 1

Author

Reinhard Zumkeller, Jan 09 2003

Keywords

• nonn
• look

Comments

A078701(a(n))=A078701(n), A078701(i)<>A078701(n), n

n + A078701(n) <= a(n) <= 2*n;

a(2^k) = 2^(k+1), as A078701(2^k) = 1.

Links

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

Crossrefs

Cf. A079432(n) = a(a(n)).

Cf. A078701.

Programs

Maple

N:= 100:
A:= Vector(N):
p:= 2:
do
  p:= nextprime(p);
  if p > N then break fi;
  R:= select(k -> A[k] = 0, [$1..N]);
  S:= select(`<=`,R,N/p);
  A[p*S]:= Vector(p*R[2..1+nops(S)]);
od:
for k from 0 to ilog2(N) do A[2^k]:= 2^(k+1) od:
convert(A,list); # Robert Israel, Oct 25 2017

Mathematica

sopf[n_] := SelectFirst[FactorInteger[n][[All, 1]], # > 2&];
a[n_] := For[p = sopf[n]; m = n+1, True, m++, If[p == sopf[m], Return[m]]];
Array[a, 100] (* Jean-François Alcover, Mar 09 2019 *)

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