A084400 a(1) = 1; for n>1, a(n) = smallest number that does not divide the product of all previous terms.

1, 2, 3, 4, 5, 7, 9, 11, 13, 16, 17, 19, 23, 25, 29, 31, 37, 41, 43, 47, 49, 53, 59, 61, 67, 71, 73, 79, 81, 83, 89, 97, 101, 103, 107, 109, 113, 121, 127, 131, 137, 139, 149, 151, 157, 163, 167, 169, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239

Offset

1,2

Comments

All numbers of the form p^(2^k) are members.

Except for the first term, same as A050376. - David Wasserman, Dec 22 2004

Also, the lexicographically earliest sequence of distinct positive integers such that the number of divisors of the product of n initial terms (for any n) is a power of 2. - Ivan Neretin, Aug 12 2015

Links

Giovanni Resta, Table of n, a(n) for n = 1..10000

Prog

(PARI) find(pv)=k = 1; while (! (pv % k), k++); return (k);
lista(nn) = print1(pv=1, ", "); for (i=1, nn, nv = find(pv); pv *= nv; print1(nv, ", ")) \\ Michel Marcus, Aug 12 2015
(PARI) A209229(n)=if(n%2, n==1, isprimepower(n))
is(n)=A209229(isprimepower(n)) || n==1 \\ Charles R Greathouse IV, Oct 19 2015
(Python)
from sympy import primepi, integer_nthroot
def A084400(n):
    def bisection(f, kmin=0, kmax=1):
        while f(kmax) > kmax: kmax <<= 1
        kmin = kmax >> 1
        while kmax-kmin > 1:
            kmid = kmax+kmin>>1
            if f(kmid) <= kmid:
                kmax = kmid
            else:
                kmin = kmid
        return kmax
    def f(x): return n-1+x-sum(primepi(integer_nthroot(x, 1<<i)[0]) for i in range(x.bit_length().bit_length()))
    return bisection(f, n, n) # Chai Wah Wu, Mar 25 2025

Crossrefs

Cf. A000040 (primes), A026416, A000028, A066724, A026477, A050376.

Sequence in context: A009087 A026477 A079852 * A050376 A280257 A050198

Adjacent sequences: A084397 A084398 A084399 * A084401 A084402 A084403

Keyword

nonn

Author

Amarnath Murthy, May 31 2003

Extensions

More terms from Patrick De Geest, Jun 05 2003

Status

approved