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A226512 a(n) = minimum of sum of orders of all elements of G, where G is a group of order n. 2
1, 3, 7, 7, 21, 13, 43, 15, 25, 31, 111, 31, 157, 57, 147, 31, 273, 43, 343, 71, 85, 133, 507, 67, 121, 183, 79, 157, 813, 177, 931, 63, 777, 307, 903, 111, 1333, 381, 235, 163, 1641, 183, 1807, 377, 525, 553, 2163, 127, 337, 171, 1911, 287, 2757, 133, 331, 351, 457, 871, 3423, 211 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

If n is prime, a(n) = A057660(n).

LINKS

G. Nebe, Table of n, a(n) for n = 1..200

Habib Amiri, S. M. Jafarian Amiri, Sum of element orders on finite groups of the same order, J. Algebra Appl. 10 (2011), no. 2, 187--190. MR2795731 (2012d:20050)

Habib Amiri, S. M. Jafarian Amiri, I. M. Isaacs, Sums of element orders in finite groups Comm. Algebra 37 (2009), no. 9, 2978--2980. MR2554185 (2010i:20022)

Y. Marefat et al., On the sum of element orders of finite simple groups, J. Algebra Applications, 12 (2013), #1350026.

EXAMPLE

For n=6 the group S_3 is optimal: it has one element of order 1, 3 of order 2, and 2 of order 3, for a total of a(6) = 13.

PROG

(MAGMA program from G. Nebe, Jun 14 2013:)

SS:=[];

for i in [1..200] do f:=[];

for j in [1..NumberOfSmallGroups(i)] do p:=0; G:=SmallGroup(i, j);

for g in G do p+:= Order(g); end for; Append(~f, p); end for;

Append(~SS, Minimum(f)); end for;

SS;

CROSSREFS

Cf. A057660.

Sequence in context: A113833 A212286 A157102 * A270307 A261480 A121172

Adjacent sequences:  A226509 A226510 A226511 * A226513 A226514 A226515

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Jun 13 2013

EXTENSIONS

More terms from G. Nebe, Jun 14 2013

STATUS

approved

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Last modified October 16 16:18 EDT 2019. Contains 328101 sequences. (Running on oeis4.)