This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A080685 #11 Apr 29 2025 04:43:34
%S A080685 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,18,19,20,21,21,22,23,24,
%T A080685 25,26,26,27,27,28,29,30,31,32,32,32,33,34,34,35,35,36,37,37,37,38,39,
%U A080685 40,41,42,42,43,44,45,45,45,45,46,46,46,47,48,49,50,50,51,51,52,52,53
%N A080685 Number of 17-smooth numbers <= n.
%C A080685 Range = primes 2 to 17. Input pn=17 in script below. Code below is much faster than the code for cross-reference. For input of n=200 13 times as fast and many times faster for larger input of n.
%H A080685 Amiram Eldar, <a href="/A080685/b080685.txt">Table of n, a(n) for n = 1..10000</a>
%t A080685 Accumulate[Table[Boole[Max[FactorInteger[n][[;; , 1]]] <= 17], {n, 100}]] (* _Amiram Eldar_, Apr 29 2025 *)
%o A080685 (PARI) smoothn(n,pn) = { for(m=1,n, pr=1; forprime(p=2,pn, pr*=p; ); ct=1; for(x=1,m, f=0; forprime(y=nextprime(pn+1),floor(x), if(x%y == 0,f=1; break) ); if(gcd(x,pr)<>1,if(f==0,ct+=1; )) ); print1(ct","); ) }
%Y A080685 Cf. A080681.
%Y A080685 Number of p-smooth numbers <= n: A070939 (p=2), A071521 (p=3), A071520 (p=5), A071604 (p=7), A071523 (p=11), A080684 (p=13), this sequence (p=17), A080686 (p=19).
%K A080685 easy,nonn
%O A080685 1,2
%A A080685 _Cino Hilliard_, Mar 02 2003