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 A100716 #38 Jan 05 2023 18:02:29 %S A100716 4,8,12,16,20,24,27,28,32,36,40,44,48,52,54,56,60,64,68,72,76,80,81, %T A100716 84,88,92,96,100,104,108,112,116,120,124,128,132,135,136,140,144,148, %U A100716 152,156,160,162,164,168,172,176,180,184,188,189,192,196,200,204,208,212 %N A100716 Numbers k such that p^p divides k for some prime p. %C A100716 Complement of A048103; A129251(a(n)) > 0; A051674 is a subsequence; A129254 = (terms a(k) such that a(k+1)=a(k)+1). - _Reinhard Zumkeller_, Apr 07 2007 %C A100716 A027748(a(n),k) <= A124010(a(n),k) for some k<=A001221(a(n)). - _Reinhard Zumkeller_, Apr 28 2012 %H A100716 Reinhard Zumkeller, <a href="/A100716/b100716.txt">Table of n, a(n) for n = 1..1000</a> %F A100716 a(n) ~ k*n with k = 1/(1 - Product(1 - p^-p)) = 3.5969959469... where the product is over all primes p. - _Charles R Greathouse IV_, Jan 24 2012 %e A100716 54 is included because 3^3 divides 54. %t A100716 fQ[n_] := Union[ Table[ #[[1]] <= #[[2]]] & /@ FactorInteger[n]][[ -1]] == True; Select[ Range[2, 215], fQ[ # ] &] (* _Robert G. Wilson v_, Dec 14 2004 *) %t A100716 f[n_] := Module[{aux=FactorInteger[n]}, Last@Union@Table[aux[[i,1]] <= aux[[i,2]], {i,Length[aux]}] == True]; Select[Range[2,215], f] (* _José María Grau Ribas_, Jan 25 2012 *) %t A100716 Rest@ Select[Range@ 216, Times @@ Boole@ Map[First@ # > Last@ # &, FactorInteger@ #] == 0 &] (* _Michael De Vlieger_, Aug 19 2016 *) %o A100716 (PARI) is(n)=forprime(p=2,default(primelimit),if(n%p^p==0,return(1));if(p^p>n,return(0))) \\ _Charles R Greathouse IV_, Jan 24 2012 %o A100716 (Haskell) %o A100716 a100716 n = a100716_list !! (n-1) %o A100716 a100716_list = filter (\x -> or $ %o A100716 zipWith (<=) (a027748_row x) (map toInteger $ a124010_row x)) [1..] %o A100716 -- _Reinhard Zumkeller_, Apr 28 2012 %o A100716 (Scheme, with Antti Karttunen's IntSeq-library) %o A100716 (define A100716 (NONZERO-POS 1 1 A129251)) %o A100716 ;; _Antti Karttunen_, Aug 18 2016 %o A100716 (Python) %o A100716 from itertools import count, islice %o A100716 from sympy import factorint %o A100716 def A100716_gen(startvalue=1): # generator of terms >= startvalue %o A100716 return filter(lambda n:any(map(lambda d:d[1]>=d[0],factorint(n).items())),count(max(startvalue,1))) %o A100716 A100716_list = list(islice(A100716_gen(),30)) # _Chai Wah Wu_, Jan 05 2023 %Y A100716 Complement: A048103. %Y A100716 Positions of nonzeros in A129251. %Y A100716 Cf. A100717, A129150, A129152. %Y A100716 Cf. A054744. %Y A100716 Cf. A051674 (a subsequence). %Y A100716 Subsequence of A276079 from which it differs for the first time at n=175, where a(175) = 628, while A276079(175) = 625, a value missing from here. %K A100716 nonn %O A100716 1,1 %A A100716 _Leroy Quet_, Dec 10 2004 %E A100716 More terms from _Robert G. Wilson v_, Dec 14 2004