A215369 Numbers n with the same f-value as n+1, where f(n) = A056239(n) = Sum_{i} i*e_i for n = Product_{i} prime(i)^e_i.

3, 5, 9, 14, 21, 27, 44, 77, 98, 104, 115, 125, 152, 247, 289, 363, 423, 455, 492, 624, 670, 714, 860, 1016, 1044, 1224, 1274, 1449, 1659, 1715, 1817, 1862, 2013, 2255, 2261, 2424, 2596, 2679, 2847, 3255, 3285, 3362, 3477, 3478, 3626, 3925, 4185, 4233, 4292

Offset: 1

Author

Alois P. Heinz, Aug 09 2012

Keywords

• nonn

Comments

Also numbers n such that both n and n+1 are in the same row of A215366.

Examples

			44 is in the sequence because 44 = 2^2 * 11 = prime(1)^2 * prime(5) => f(44) = 1*2+5 = 7 and 44+1 = 45 = 3^2*5 = prime(2)^2 * prime(3) => f(45) = 2*2+3 = 7.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A056239, A088850, A215366.

Programs

Maple

f:= n-> add(numtheory[pi](i[1])*i[2], i=ifactors(n)[2]):
a:= proc(n) option remember; local k;
      for k from 1+ `if`(n=1, 0, a(n-1))
      while f(k)<>f(k+1) do od; k
    end:
seq(a(n), n=1..70);

Mathematica

f[n_] := Sum[PrimePi[i[[1]]]*i[[2]], {i, FactorInteger[n]}];
a[n_] := a[n] = (For[k = 1 + If[n==1, 0, a[n-1]], f[k] != f[k+1], k++]; k);
Array[a, 70] (* Jean-François Alcover, Mar 22 2017, translated from Maple *)