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 A252117 Triangle read by row: T(n,k), n>=1, k>=1, in which column k lists the numbers of A000716 multiplied by A000330(k), and the first element of column k is in row A000217(k). 1
 1, 3, 9, 5, 22, 15, 51, 45, 108, 110, 14, 221, 255, 42, 429, 540, 126, 810, 1105, 308, 1479, 2145, 714, 30, 2640, 4050, 1512, 90, 4599, 7395, 3094, 270, 7868, 13200, 6006, 660, 13209, 22995, 11340, 1530, 21843, 39340, 20706, 3240, 55, 35581, 66045, 36960, 6630, 165, 57222, 109215, 64386, 12870, 495 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Conjecture: gives an identity for sigma. Alternating sum of row n equals the sum of divisors of n, i.e., sum_{k=1..A003056(n)} (-1)^(k-1)*T(n,k) = A000203(n). Row n has length A003056(n) hence column k starts in row A000217(k). Column 1 is A000716, but here the offset is 1 not 0. The 1st element of column k is A000330(k). The 2nd element of column k is A059270(k). The 3rd element of column k is A220443(k). The partial sums of column k give the k-th column of A249120. This triangle has been constructed after Mircea Merca's formula for A000203. LINKS EXAMPLE Triangle begins: 1; 3, 9,           5; 22,         15, 51,         45, 108,       110,     14; 221,       255,     42, 429,       540,    126, 810,      1105,    308, 1479,     2145,    714,     30; 2640,     4050,   1512,     90, 4599,     7395,   3094,    270, 7868,    13200,   6006,    660, 13209,   22995,  11340,   1530, 21843,   39340,  20706,   3240,    55; 35581,   66045,  36960,   6630,   165, 57222,  109215,  64386,  12870,   495, 90882,  177905, 110152,  24300,  1210, 142769, 286110, 184926,  44370,  2805, 221910, 454410, 305802,  79200,  5940, 341649, 713845, 498134, 137970, 12155,    91; ... For n = 6 the divisors of 6 are 1, 2, 3, 6, so the sum of divisors of 6 is 1 + 2 + 3 + 6 = 12. On the other hand, the 6th row of the triangle is 108, 110, 14, so the alternating row sum is 108 - 110 + 14 = 12, equaling the sum of divisors of 6. For n = 15 the divisors of 15 are 1, 3, 5, 15, so the sum of divisors of 15 is 1 + 3 + 5 + 15 = 24. On the other hand, the 15th row of the triangle is 21843, 39340, 20706, 3240, 55, so the alternating row sum is 21843 - 39340 + 20706 - 3240 + 55 = 24, equaling the sum of divisors of 15. CROSSREFS Cf. A000203, A000217, A000330, A000716, A003056, A059270, A196020, A220443, A238442, A249120. Sequence in context: A088898 A143218 A262024 * A103934 A186814 A077384 Adjacent sequences:  A252114 A252115 A252116 * A252118 A252119 A252120 KEYWORD nonn,tabf AUTHOR Omar E. Pol, Dec 14 2014 STATUS approved

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Last modified February 27 15:59 EST 2020. Contains 332307 sequences. (Running on oeis4.)