A384223 Irregular triangle read by rows: T(n,k) is the sum of the k-th odd divisor and the next even divisors that are less than the next odd divisor of n, with n >= 1, k >= 1.
1, 3, 1, 3, 7, 1, 5, 3, 9, 1, 7, 15, 1, 3, 9, 3, 15, 1, 11, 3, 25, 1, 13, 3, 21, 1, 3, 5, 15, 31, 1, 17, 3, 9, 27, 1, 19, 7, 35, 1, 3, 7, 21, 3, 33, 1, 23, 3, 57, 1, 5, 25, 3, 39, 1, 3, 9, 27, 7, 49, 1, 29, 3, 3, 21, 45, 1, 31, 63, 1, 3, 11, 33, 3, 51, 1, 5, 7, 35, 3, 13, 75, 1, 37, 3, 57, 1, 3, 13, 39, 7, 83
Offset: 1
Examples
Triangle begins: 1; 3; 1, 3; 7; 1, 5; 3, 9; 1, 7; 15; 1, 3, 9; 3, 15; 1, 11; 3, 25; 1, 13; 3, 21; 1, 3, 5, 15; 31; ... For n = 30 the list of divisors of 30 is [1, 2, 3, 5, 6, 10, 15, 30]. There are four sublists of divisors whose first term is odd. They are [1, 2], [3], [5, 6, 10], [15, 30]. The sum of the divisors in the sublists are respectively [3, 3, 21, 45], the same as the 30th row of the triangle.
Crossrefs
Programs
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PARI
row(n) = {my(d = divisors(n), res = vector(#d / (valuation(n, 2)+1)), t = 1, s = 1); for(i = 2, #d, if(bitand(d[i], 1), res[t] = s; t++; s = d[i], s += d[i])); res[#res] = s; res} \\ David A. Corneth, Jun 08 2025
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