A094222 -id:A094222 - cp's OEIS frontend

A160649 a(1)=2. a(n) = a(n-1) + A001222(a(n-1)); where A001222(m) is the sum of prime-factorization exponents of m (or, A001222(m) is the number of primes dividing m, with multiplicity).

2, 3, 4, 6, 8, 11, 12, 15, 17, 18, 21, 23, 24, 28, 31, 32, 37, 38, 40, 44, 47, 48, 53, 54, 58, 60, 64, 70, 73, 74, 76, 79, 80, 85, 87, 89, 90, 94, 96, 102, 105, 108, 113, 114, 117, 120, 125, 128, 135, 139, 140, 144, 150, 154, 157, 158, 160, 166, 168, 173, 174, 177, 179

Offset: 1

Leroy Quet, May 21 2009

nonn

A001222(a(n)) = A160650(n) = a(n+1) - a(n).

G. C. Greubel, Table of n, a(n) for n = 1..10000

Cf. A001222, A094222, A160650.

NestList[# + PrimeOmega[#] &, 2, 100] (* Zak Seidov, Feb 15 2015 *)

lista(nn) = {print1(a=2, ", "); for (n=2, nn, a += bigomega(a); print1(a, ", "););} \\ Michel Marcus, May 04 2018

Extended by Ray Chandler, Jun 16 2009

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.

Original entry on oeis.org

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

Samuel Frankmartin-Sebastian Wiethüchter, May 01 2020

nonn

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

			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;

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

Cf. A094222.

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);

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

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

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

cp's OEIS Frontend

A160649 a(1)=2. a(n) = a(n-1) + A001222(a(n-1)); where A001222(m) is the sum of prime-factorization exponents of m (or, A001222(m) is the number of primes dividing m, with multiplicity).

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

PARI

Extensions