A346378 a(n) is the least k such that there are exactly n numbers i with A075254(i) = k.

2, 1, 14, 59, 143, 239, 1079, 2519, 1439, 7559, 17639, 4319, 14399, 70559, 55439, 113399, 120959, 166319, 205919, 332639, 760319, 554399, 907199, 277199, 720719, 2162159, 3245759, 4324319, 2494799, 5266799, 5765759, 9172799, 8315999, 15724799, 16853759, 21067199

Offset: 0

Author

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

Keywords

• nonn

Comments

a(n) is the least solution k to A346377(k) = n.

Examples

			a(3) = 59 because there are 3 solutions to A075254(k) = 59, namely
  A075254(38) = 38+2+19 = 59
  A075254(44) = 44+2+2+11 = 59
  A075254(48) = 48+2+2+2+2+3 = 59
and no number < 59 has exactly 3 solutions.
		

Crossrefs

Cf. A075254, A346377

Programs

Maple

f:= proc(n) local t; add(t[1]*t[2],t=ifactors(n)[2])+n end proc:
N:= 10^6: # for terms <= 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:
m:= max(V):
A:= Array(0..m):
for i from 1 to N do
  if A[V[i]] = 0 then A[V[i]]:= i fi
od:
convert(A,list);

Mathematica

f[1] = 1; f[n_] := n + Plus @@ Times @@@ FactorInteger[n]; m = 10^7; v = Table[0, {m}]; Do[i = f[n]; If[i <= m, v[[i]]++], {n, 1, m}]; TakeWhile[Table[ FirstPosition[v, k][[1]], {k, 0, Max[v]}], NumericQ] (* Amiram Eldar, Jul 14 2021 *)