cp's OEIS Frontend

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.

A061743 Numbers k such that k! is divisible by (k+1)^2.

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%I A061743 #17 Oct 17 2024 14:46:14
%S A061743 11,14,15,17,19,20,23,24,26,27,29,31,32,34,35,38,39,41,43,44,47,48,49,
%T A061743 50,51,53,54,55,56,59,62,63,64,65,67,68,69,71,74,75,76,77,79,80,83,84,
%U A061743 86,87,89,90,91,92,94,95,97,98,99,101,103,104,107,109,110,111,113,114
%N A061743 Numbers k such that k! is divisible by (k+1)^2.
%H A061743 Harry J. Smith, <a href="/A061743/b061743.txt">Table of n, a(n) for n = 1..2000</a>
%F A061743 a(n) = A264828(n+3)-1. Complement of {A178156} - 1. - _Chai Wah Wu_, Oct 17 2024
%t A061743 Select[Range[120], IntegerQ[ #!/(# + 1)^2] &]
%o A061743 (PARI) { n=0; f=1; for (a=1, 2588, f*=a; if (f%(a + 1)^2 == 0, write("b061743.txt", n++, " ", a)) ) } \\ _Harry J. Smith_, Jul 27 2009
%o A061743 (PARI) isok(k) = !(k! % (k+1)^2); \\ _Michel Marcus_, Jul 01 2018
%o A061743 (Python)
%o A061743 from sympy import primepi
%o A061743 def A061743(n):
%o A061743     def f(x): return int(n+2+primepi(x+1)+primepi(x+1>>1))
%o A061743     m, k = n, f(n)
%o A061743     while m != k: m, k = k, f(k)
%o A061743     return m # _Chai Wah Wu_, Oct 17 2024
%Y A061743 Cf. A001751, A060462, A178156, A264848.
%K A061743 nonn
%O A061743 1,1
%A A061743 _Robert G. Wilson v_, Jun 21 2001