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 A249120 Triangle read by rows: T(n,k), n>=1, k>=1, in which column k lists the numbers of A210843 multiplied by A000330(k), and the first element of column k is in row A000217(k). 1
 1, 4, 13, 5, 35, 20, 86, 65, 194, 175, 14, 415, 430, 56, 844, 970, 182, 1654, 2075, 490, 3133, 4220, 1204, 30, 5773, 8270, 2716, 120, 10372, 15665, 5810, 390, 18240, 28865, 11816, 1050, 31449, 51860, 23156, 2580, 53292, 91200, 43862, 5820, 55, 88873, 157245, 80822, 12450, 220, 146095, 266460, 145208, 25320, 715 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Conjecture: gives an identity for the sum of all divisors of all positive integers <= n. Alternating sum of row n equals A024916(n), i.e., sum_{k=1..A003056(n))} (-1)^(k-1)*T(n,k) = A024916(n). Row n has length A003056(n) hence the first element of column k is in row A000217(k). Column 1 is A210843. Column k lists the partial sums of the k-th column of triangle A252117 which gives an identity for sigma. The first element of column k is A000330(k). The second element of column k is A002492(k). LINKS EXAMPLE Triangle begins: 1; 4; 13,           5; 35,          20; 86,          65; 194,        175,      14; 415,        430,      56; 844,        970,     182; 1654,      2075,     490; 3133,      4220,    1204,     30; 5773,      8270,    2716,    120; 10372,    15665,    5810,    390; 18240,    28865,   11816,   1050; 31449,    51860,   23156,   2580; 53292,    91200,   43862,   5820,    55; 88873,   157245,   80822,  12450,   220; 146095,  266460,  145208,  25320,   715; 236977,  444365,  255360,  49620,  1925; 379746,  730475,  440286,  93990,  4730; 601656, 1184885,  746088, 173190, 10670; 943305, 1898730, 1244222, 311160, 22825,   91; ... For n = 6 the sum of all divisors of all positive integers <= 6 is [1] + [1+2] + [1+3] + [1+2+4] + [1+5] + [1+2+3+6] = 1 + 3 + 4 + 7 + 6 + 12 = 33. On the other hand the 6th row of triangle is 194, 175, 14, so the alternating row sum is 194 - 175 + 14 = 33, equaling the sum of all divisors of all positive integers <= 6. CROSSREFS Cf. A000203, A000217, A000330, A002492, A003056, A024916, A195825, A196020, A210843, A211970, A236104, A252117. Sequence in context: A320030 A191509 A218356 * A170844 A051432 A064461 Adjacent sequences:  A249117 A249118 A249119 * A249121 A249122 A249123 KEYWORD nonn,tabf AUTHOR Omar E. Pol, Dec 14 2014 STATUS approved

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Last modified January 24 16:47 EST 2020. Contains 331209 sequences. (Running on oeis4.)