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

Author

Amarnath Murthy, May 31 2003

Keywords

• nonn

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

Crossrefs

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

Programs

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<Chai Wah Wu, Mar 25 2025

Extensions

More terms from Patrick De Geest, Jun 05 2003