A127669 Number of numbers mapped to A127668(n) with the map described there.

1, 1, 2, 1, 2, 1, 3, 2, 2, 1, 3, 1, 2, 2, 5, 1, 3, 1, 3, 2, 2, 1, 5, 2, 2, 3, 3, 1, 3, 2, 7, 2, 2, 2, 5, 1, 2, 2, 5, 1, 3, 1, 3, 3, 2, 1, 7, 2, 3, 2, 3, 1, 5, 2, 5, 2, 2, 1, 5, 1, 3, 3, 11, 2, 3, 1, 3, 2, 3, 1, 7, 2, 2, 3, 3, 2, 3, 2, 7, 5, 2, 1, 5, 2, 2, 2, 5, 1, 5, 2, 3, 2, 2, 2, 11, 1, 3, 3, 5

Offset: 2

Author

Wolfdieter Lang Jan 23 2007

Keywords

• nonn
• easy
• base

Comments

This is not A008481(n), n>=2, which starts similarly, but differs, beginning with n=24.

Examples

			a(4)=2 because two numbers are mapped to 11= A127668(4), namely n=p(1)*p(1)=4 and n=p(11)=31. p(n)=A000041(n) (partition numbers).
a(24)=5 but A008481(24)=4.
The five numbers mapped to A127668(24)= 2111 are: 18433, 2594, 2263, 292, 24.
		

Links

• Robert Israel, Table of n, a(n) for n = 2..10000

Crossrefs

Cf. A008481, A127668.

Programs

Maple

f:= proc(n) local S;
   nops(g(sprintf("%d",n)))
end proc:
g:= proc(s) option remember;
    local S,m,k1;
    if s[1] = "0" then return {} fi;
    S:= {[parse(s)]};
    for m from 1 to length(s)-1 do
      k1:= parse(s[1..m]);
      S:= S union map(t -> [k1,op(t)], select(r -> r[1] <= k1, procname(s[m+1..-1])));
    od;
    S;
end proc:
h:= proc(n) local F;
  F:= map(t -> numtheory:-pi(t[1])$t[2], sort(ifactors(n)[2],(a,b) -> a[1] > b[1]));
  parse(cat(op(F)))
end proc:
seq(f(h(i)),i=2..100); # Robert Israel, Dec 08 2024

Formula

a(n) <= pa(Length( A127668(n))), n>=2. Length gives the number of digits and pa(k):=A000041(k) (partition numbers). (It was originally claimed that this is equality, but that is not correct. - Franklin T. Adams-Watters, May 21 2014)

Extensions

Edited by Franklin T. Adams-Watters, May 21 2014

Corrected by Robert Israel, Dec 08 2024