A330908 a(n+1) = a(n) + (number of divisors of a(n) that are not divisors of other divisors of a(n)) for n>1; a(1)=1.

1, 2, 4, 6, 9, 11, 13, 15, 18, 21, 24, 27, 29, 31, 33, 36, 39, 42, 46, 49, 51, 54, 57, 60, 64, 66, 70, 74, 77, 80, 83, 85, 88, 91, 94, 97, 99, 102, 106, 109, 111, 114, 118, 121, 123, 126, 130, 134, 137, 139, 141, 144, 147, 150, 154, 158, 161, 164, 167, 169

Offset: 1

Author

Samuel Frankmartin-Sebastian Wiethüchter, May 01 2020

Keywords

• nonn

Comments

The sequence is similar built like A094222 but includes 1 as divisor or adds 1 to the number of distinct primes dividing a(n).

Examples

			For n = 2 calculate a(2)= a(2-1) + A083399(a(2-1))= 1 + 1 = 2;
For n = 3 a(3)=a(2) + A083399(a(2))= 2 + 2 = 4;
For n = 4 a(4)=a(3) + A083399(a(3))= 4 + 2 = 6;
For n = 5 a(5)=a(4) + A083399(a(4))= 6 + 3 = 9;
		

Links

• Samuel Frankmartin-Sebastian Wiethüchter, Table of n, a(n) for n = 1..5000

Crossrefs

Cf. A094222.

Programs

Maple

A330908 := proc(n) option remember;
    if n < 2 then
        n
    else
        procname(n-1)+A083399(procname(n-1))
    end if;
end proc:
seq(A330908(n), n=1..30);

Mathematica

a[1] = 1; a[n_] := a[n] = a[n - 1] + PrimeNu[a[n - 1]] + 1; Array[a, 60] (* Amiram Eldar, May 01 2020 *)

PARI

f(n) = omega(n) + 1; \\ A083399
lista(nn) = {my(a=1, va = List(a)); for (n=2, nn, a = a+f(a); listput(va, a);); Vec(va);} \\ Michel Marcus, May 03 2020

Formula

a(n) = a(n-1) + A083399(a(n-1)) for n>1.