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The smallest positive integer which can be written as a sum of consecutive positive integers in 12 ways is 945.
As it turns out, 945 can be writen as a sum in 15 ways, listed below).
Bryan gives a proof that 945 is the smallest here.
945 in 2 terms = 472+473
945 in 3 terms = 314+315+316
945 in 5 terms = 187+188+189+190+191
945 in 6 terms = 155+156+157+158+159+160
945 in 7 terms = 132+133+134+135+136+137+138
945 in 9 terms = sum of 101 to 109
945 in 10 terms = sum of 90 to 99
945 in 14 terms = sum of 61 to 74
945 in 15 terms = sum of 56 to 70
945 in 18 terms = sum of 44 to 61
945 in 21 terms = sum of 35 to 55
945 in 27 terms = sum of 22 to 48
945 in 30 terms = sum of 17 to 46
945 in 35 terms = sum of 10 to 44
945 in 42 terms = sum of 2 to 43 |
