A281365 - OEIS

%I #8 Jul 02 2018 14:11:38

%S 1,2,3,3,4,6,5,6,5,8,5,10,7,10,14,9,6,10,7,14,17,10,5,24,7,14,7,17,7,

%T 28,9,12,17,12,24,17,10,14,25,36,9,34,9,17,24,10,5,38,9,14,22,25,7,14,

%U 24,42,24,14,5,56,13,18,39,15,40,34,9,22,17,48,9,42

%N Number of distinct multiplicative groups mod n, allowing any choice of identity element.

%H Andrew Howroyd, <a href="/A281365/b281365.txt">Table of n, a(n) for n = 1..1000</a>

%H Keith F. Lynch, <a href="/A281365/a281365.txt">List of all such groups through n=1000</a>. For each group, the first two numbers specify n and the identity element, then the group elements are listed after the colon.

%F a(n) = 1 + Sum_{d|n, gcd(d, n/d)==1} A272831(d). - _Andrew Howroyd_, Jul 02 2018

%e For instance a(10) = 8 because the following are multiplicative groups mod 10: {0*} {1*} {5*} {6*} {4,6*} {2,4,6*,8} {1*,9} {1*,3,7,9}, with identity elements marked with asterisks.

%Y Cf. A272831.

%K nonn

%O 1,2

%A _Keith F. Lynch_, Apr 30 2016