A281365 Number of distinct multiplicative groups mod n, allowing any choice of identity element.

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

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_{d|n, 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