A346377 a(n) is the number of solutions k to A075254(k) = n.

1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 0, 2, 1, 0, 1, 0, 1, 0, 0, 1, 2, 1, 0, 2, 0, 0, 1, 0, 1, 0, 1, 1, 2, 1, 0, 1, 1, 1, 1, 1, 0, 0, 0, 2, 2, 0, 0, 0, 1, 0, 1, 1, 1, 1, 0, 1, 3, 0, 0, 2, 1, 0, 1, 0, 0, 0, 2, 0, 3, 1, 0, 1, 0, 2, 0, 0, 1, 0, 0, 2, 1, 2, 0, 1, 0, 1, 2, 0, 0, 0, 2, 1, 3, 1, 0, 1, 1

Offset

1,14

Comments

a(n) is the number of k such that k + A001414(k) = n.

Links

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

Example

a(14) = 2 because there are two solutions to A075254(k) = 14, namely
A075254(7) = 7+7 = 14
A075254(8) = 8+2+2+2 = 14

Maple

f:= proc(n) local t; add(t[1]*t[2], t=ifactors(n)[2])+n end proc:
N:= 100: # for a(1)..a(N)
V:= Vector(N):
for n from 1 to N do
  v:= f(n);
  if v <= N then V[v]:= V[v]+1 fi
od:
convert(V[1..N], list);

Mathematica

f[1] = 1; f[n_] := n + Plus @@ Times @@@ FactorInteger[n]; m = 100; v = Table[0, {m}]; Do[i = f[n]; If[i <= m, v[[i]]++], {n, 1, m}]; v (* Amiram Eldar, Jul 14 2021 *)

Crossrefs

Cf. A001414, A075254, A346378.

Sequence in context: A144961 A144627 A135929 * A338757 A080733 A080732

Adjacent sequences: A346374 A346375 A346376 * A346378 A346379 A346380

Keyword

nonn

Author

J. M. Bergot and Robert Israel, Jul 14 2021

Status

approved