cp's OEIS Frontend

A332271 a(n) is the smallest positive integer that is not a divisor of the n-th highly composite number (A002182).

%I A332271 #104 Aug 03 2025 23:24:11
%S A332271 2,3,3,4,5,5,5,5,7,7,7,7,7,7,9,8,9,11,11,11,11,11,11,11,13,11,11,13,
%T A332271 13,13,13,13,13,13,13,13,13,17,16,17,17,17,17,17,17,17,17,17,17,17,17,
%U A332271 17,19,17,19,19,19,19,19,19,19,19,19,19,23,19,19,23,23,19,23,23,23,23,23,23
%N A332271 a(n) is the smallest positive integer that is not a divisor of the n-th highly composite number (A002182).
%C A332271 a(1)=2 and a(2)=3 are the only terms greater than the n-th highly composite number.
%C A332271 Terms are powers of primes (A000961). - _David A. Corneth_, Jul 12 2020
%C A332271 There are only 8 nonprimes in first 779674 terms: 4, 9, 8, 9, 16, 25, 25, 32. - _Jason A. Doucette_, Jul 20 2025
%H A332271 Jason A. Doucette, <a href="/A332271/b332271.txt">Table of n, a(n) for n = 1..20000</a>
%H A332271 Matthew Doucette, <a href="http://xona.com/antiprimefactors/">Lowest Unused Anti-Prime (Highly Composite Number) Factors</a>
%H A332271 Matthew Doucette, <a href="http://xona.com/antiprimes/">Highly Composite Numbers (Anti-Primes)</a> (first missing number from factorizations)
%H A332271 Matthew Doucette, <a href="https://youtu.be/f7EKdzViIQ8">Calculating Highly Composite Numbers (Anti-Primes)</a> (first missing number from factorizations)
%F A332271 a(n) = A007978(A002182(n)).
%e A332271 a(1) = 2 = least non-divisor of 1.
%e A332271 a(2) = 3 = least non-divisor of 2.
%e A332271 a(3) = 3 = least non-divisor of 4.
%e A332271 a(4) = 4 = least non-divisor of 6.
%e A332271 a(5) = 5 = least non-divisor of 12.
%e A332271 ...
%o A332271 (PARI) nondiv(n) = {for (k=1, n+1, if (n % k, return (k)););} \\ A007978
%o A332271 lista(nn) = {my(list=List([1]), r=1); forstep(n=2, nn, 2, if(numdiv(n)>r, r=numdiv(n); listput(list, n));); apply(x->nondiv(x), Vec(list));} \\ _Michel Marcus_, Jun 10 2020
%Y A332271 Cf. A000961, A002182, A007978.
%K A332271 nonn
%O A332271 1,1
%A A332271 _Matthew Doucette_, Jun 05 2020
%E A332271 a(67)-a(71) from _David A. Corneth_, Jul 12 2020
%E A332271 a(72) onward from _Jason A. Doucette_, Jul 20 2025