A061743 - OEIS

%I #17 Oct 17 2024 14:46:14

%S 11,14,15,17,19,20,23,24,26,27,29,31,32,34,35,38,39,41,43,44,47,48,49,

%T 50,51,53,54,55,56,59,62,63,64,65,67,68,69,71,74,75,76,77,79,80,83,84,

%U 86,87,89,90,91,92,94,95,97,98,99,101,103,104,107,109,110,111,113,114

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

%H Harry J. Smith, <a href="/A061743/b061743.txt">Table of n, a(n) for n = 1..2000</a>

%F a(n) = A264828(n+3)-1. Complement of {A178156} - 1. - _Chai Wah Wu_, Oct 17 2024

%t Select[Range[120], IntegerQ[ #!/(# + 1)^2] &]

%o (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 (PARI) isok(k) = !(k! % (k+1)^2); \\ _Michel Marcus_, Jul 01 2018

%o (Python)

%o from sympy import primepi

%o def A061743(n):

%o     def f(x): return int(n+2+primepi(x+1)+primepi(x+1>>1))

%o     m, k = n, f(n)

%o     while m != k: m, k = k, f(k)

%o     return m # _Chai Wah Wu_, Oct 17 2024

%Y Cf. A001751, A060462, A178156, A264848.

%K nonn

%O 1,1

%A _Robert G. Wilson v_, Jun 21 2001