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A132191
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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) }.
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9
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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; internal format)
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OFFSET
| 0,3
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LINKS
| Max Alekseyev, First 20 rows and columns of table
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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, ...
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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
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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
Sequence in context: A142978 A152060 A093190 * A094437 A172431 A053123
Adjacent sequences: A132188 A132189 A132190 * A132192 A132193 A132194
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KEYWORD
| nonn,tabl
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Dec 01 2007, based on email from Max Alekseyev, Nov 08 2007
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EXTENSIONS
| More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Apr 26 2008
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