cp's OEIS Frontend

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

%I A084400 #26 Apr 22 2025 03:51:07
%S A084400 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,
%T A084400 71,73,79,81,83,89,97,101,103,107,109,113,121,127,131,137,139,149,151,
%U A084400 157,163,167,169,173,179,181,191,193,197,199,211,223,227,229,233,239
%N A084400 a(1) = 1; for n>1, a(n) = smallest number that does not divide the product of all previous terms.
%C A084400 All numbers of the form p^(2^k) are members.
%C A084400 Except for the first term, same as A050376. - _David Wasserman_, Dec 22 2004
%C A084400 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
%H A084400 Giovanni Resta, <a href="/A084400/b084400.txt">Table of n, a(n) for n = 1..10000</a>
%o A084400 (PARI) find(pv)=k = 1; while (! (pv % k), k++); return (k);
%o A084400 lista(nn) = print1(pv=1, ", "); for (i=1, nn, nv = find(pv); pv *= nv; print1(nv, ", ")) \\ _Michel Marcus_, Aug 12 2015
%o A084400 (PARI) A209229(n)=if(n%2, n==1, isprimepower(n))
%o A084400 is(n)=A209229(isprimepower(n)) || n==1 \\ _Charles R Greathouse IV_, Oct 19 2015
%o A084400 (Python)
%o A084400 from sympy import primepi, integer_nthroot
%o A084400 def A084400(n):
%o A084400     def bisection(f,kmin=0,kmax=1):
%o A084400         while f(kmax) > kmax: kmax <<= 1
%o A084400         kmin = kmax >> 1
%o A084400         while kmax-kmin > 1:
%o A084400             kmid = kmax+kmin>>1
%o A084400             if f(kmid) <= kmid:
%o A084400                 kmax = kmid
%o A084400             else:
%o A084400                 kmin = kmid
%o A084400         return kmax
%o A084400     def f(x): return n-1+x-sum(primepi(integer_nthroot(x,1<<i)[0]) for i in range(x.bit_length().bit_length()))
%o A084400     return bisection(f,n,n) # _Chai Wah Wu_, Mar 25 2025
%Y A084400 Cf. A000040 (primes), A026416, A000028, A066724, A026477, A050376.
%K A084400 nonn
%O A084400 1,2
%A A084400 _Amarnath Murthy_, May 31 2003
%E A084400 More terms from _Patrick De Geest_, Jun 05 2003