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.

A281856 One fourth of the order of the abelian non-cyclic groups (Z/A033949(n)*Z)^x.

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%I A281856 #17 Feb 25 2025 14:56:13
%S A281856 1,1,2,2,2,3,2,3,2,4,5,6,3,6,4,3,5,6,4,8,6,10,6,9,4,9,8,12,5,8,11,6,6,
%T A281856 10,9,15,6,8,6,16,14,10,6,18,11,15,18,8,15,10,8,12,12,9,10,18,12,9,22,
%U A281856 14,18,24,8,20,15,9,16,21,12,10,27,18,16,11,12,23
%N A281856 One fourth of the order of the abelian non-cyclic groups (Z/A033949(n)*Z)^x.
%C A281856 a(n) is one fourth of the row product of the irregular triangle A281854.
%F A281856 a(n) = A000010(A033949(n))/4, n >= 1.
%t A281856 EulerPhi@ Select[Range[2, 130], ! IntegerQ@ PrimitiveRoot@ # &]/4 (* _Michael De Vlieger_, Feb 02 2017 *)
%o A281856 (Python)
%o A281856 from sympy import primepi, integer_nthroot, totient
%o A281856 def A281856(n):
%o A281856     def f(x): return int(n+1+(x>=2)+(x>=4)+sum(primepi(integer_nthroot(x,k)[0])-1 for k in range(1,x.bit_length()))+sum(primepi(integer_nthroot(x>>1,k)[0])-1 for k in range(1,x.bit_length()-1)))
%o A281856     m, k = n, f(n)
%o A281856     while m != k: m, k = k, f(k)
%o A281856     return totient(m)>>2 # _Chai Wah Wu_, Feb 25 2025
%Y A281856 Cf. A000010, A033949, A060679, A281854.
%K A281856 nonn
%O A281856 1,3
%A A281856 _Wolfdieter Lang_, Feb 02 2017