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 A132191 Square array a(m,n) read by antidiagonals, defined by A000010(n)*a(m,n) = Sum_{k=1..n, gcd(k,n)=1} m^{ Sum_{d|n} A000010(d)/ (multiplicative order of k modulo d) }. 13
 1, 1, 2, 1, 4, 3, 1, 6, 9, 4, 1, 12, 18, 16, 5, 1, 12, 54, 40, 25, 6, 1, 40, 72, 160, 75, 36, 7, 1, 28, 405, 280, 375, 126, 49, 8, 1, 96, 390, 2176, 825, 756, 196, 64, 9, 1, 104, 1944, 2800, 8125, 2016, 1372, 288, 81, 10, 1, 280, 3411, 17920, 13175, 23976, 4312, 2304, 405 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS From Andrew Howroyd, Apr 22 2017: (Start) Number of step shifted (decimated) sequences of length n using a maximum of m different symbols. See A056371 for an explanation of step shifts. - Number of mappings with domain {0..n-1} and codomain {1..m} up to equivalence.  Mappings A and B are equivalent if there is a d, prime to n, such that A(i) = B(i*d mod n) for i in {0..n-1}. (End) LINKS Vincenzo Librandi, Table of n, a(n) for n = 1..1830 Max Alekseyev, First 20 rows and columns of table R. C. Titsworth, Equivalence classes of periodic sequences, Illinois J. Math., 8 (1964), 266-270. EXAMPLE Array begins: 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, ... 2, 4, 6, 12, 12, 40, 28, 96, 104, 280, 216, 1248, 704, 2800, 4344, 8928, 8232, 44224, 29204, 136032, ... 3, 9, 18, 54, 72, 405, 390, 1944, 3411, 14985, 17802, 139968, 133104, 798525, 1804518, 5454378, 8072532, 64599849, 64573626, 437732424, ... 4, 16, 40, 160, 280, 2176, 2800, 17920, 44224, 263296, 419872, 4280320, 5594000, 44751616, 134391040, 539054080, 1073758360, 11453771776, 15271054960, 137575813120, ... 5, 25, 75, 375, 825, 8125, 13175, 103125, 327125, 2445625, 4884435, 61640625, 101732425, 1017323125, 3816215625, 19104609375, 47683838325, 635787765625, 1059638680675, 11924780390625, ... MATHEMATICA a[m_, n_] := (1/EulerPhi[n])*Sum[If[GCD[k, n]==1, m^DivisorSum[n, EulerPhi[#] / MultiplicativeOrder[k, #]&], 0], {k, 1, n}]; Table[a[m-n+1, n], {m, 1, 15}, {n, m, 1, -1}] // Flatten (* Jean-François Alcover, Dec 01 2015 *) PROG (PARI) for(i=1, 15, for(m=1, i, n=i-m+1; print1(sum(k=1, n, if(gcd(k, n)==1, m^sumdiv(n, d, eulerphi(d)/znorder(Mod(k, d))), 0))/eulerphi(n)", "))) \\ Herman Jamke (hermanjamke(AT)fastmail.fm), Apr 26 2008 CROSSREFS Row m=2 is A056371 Row m=3 is A056372 Row m=4 is A056373 Row m=5 is A056374 Row m=6 is A056375 Column n=2 is A000290 Column n=3 is A002411 Column n=4 is A019582 Cf. A285522, A285548. Sequence in context: A142978 A152060 A093190 * A094437 A172431 A053123 Adjacent sequences:  A132188 A132189 A132190 * A132192 A132193 A132194 KEYWORD nonn,tabl AUTHOR N. J. A. Sloane, Dec 01 2007, based on email from Max Alekseyev, Nov 08 2007 EXTENSIONS More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Apr 26 2008 Offset corrected by Andrew Howroyd, Apr 20 2017 STATUS approved

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Last modified December 11 02:55 EST 2018. Contains 318049 sequences. (Running on oeis4.)