

A281365


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


2



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, 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, 24, 42, 24, 14, 5, 56, 13, 18, 39, 15, 40, 34, 9, 22, 17, 48, 9, 42
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,2


LINKS

Andrew Howroyd, Table of n, a(n) for n = 1..1000
Keith F. Lynch, List of all such groups through n=1000. For each group, the first two numbers specify n and the identity element, then the group elements are listed after the colon.


FORMULA

a(n) = 1 + Sum_{dn, gcd(d, n/d)==1} A272831(d).  Andrew Howroyd, Jul 02 2018


EXAMPLE

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.


CROSSREFS

Cf. A272831.
Sequence in context: A200469 A200251 A207100 * A304705 A131187 A099072
Adjacent sequences: A281362 A281363 A281364 * A281366 A281367 A281368


KEYWORD

nonn


AUTHOR

Keith F. Lynch, Apr 30 2016


STATUS

approved



