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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
OFFSET
1,2
LINKS
Habib Amiri and 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, and 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.
FORMULA
If p is prime, a(p) = A057660(p).
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
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Jun 13 2013
EXTENSIONS
More terms from G. Nebe, Jun 14 2013
STATUS
approved