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A113470
Triangle read by rows: n-th row is the smallest set of n numbers in arithmetic progression with the same number of divisors.
6
1, 2, 3, 3, 5, 7, 5, 11, 17, 23, 5, 11, 17, 23, 29, 7, 37, 67, 97, 127, 157, 35, 65, 95, 125, 155, 185, 215, 635, 707, 779, 851, 923, 995, 1067, 1139, 635, 707, 779, 851, 923, 995, 1067, 1139, 1211, 199, 409, 619, 829, 1039, 1249, 1459, 1669, 1879, 2089, 3841, 3973
OFFSET
1,2
COMMENTS
In this sequence "smallest" means that the last term of the arithmetic progression is minimized and if there is still a choice then we minimize the common difference of the arithmetic progression.
FORMULA
T(n,k) = A090547(n) + (k-1)*A090549(n). - R. J. Mathar, May 11 2007
EXAMPLE
From M. F. Hasler, Jan 02 2020: (Start)
The triangle starts
n | row n
---+------------
1 | 1,
2 | 2, 3,
3 | 3, 5, 7,
4 | 5, 11, 17, 23,
5 | 5, 11, 17, 23, 29,
6 | 7, 37, 67, 97, 127, 157,
7 | 35, 65, 95, 125, 155, 185, 215,
8 | 635, 707, 779, 851, 923, 995, 1067, 1139,
9 | 635, 707, 779, 851, 923, 995, 1067, 1139, 1211,
10 | 199, 409, 619, 829, 1039, 1249, 1459, 1669, 1879, 2089,
11 | 3841, 3973, ...
Most rows so far consist of primes with 2 divisors, rows 7, 8, 9 and 11 have squarefree semiprimes with 4 divisors.
Row 10 is A033168; also row 10 of A086786, A133276 and A133277. (End)
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
David Wasserman, Jan 08 2006
STATUS
approved