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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.

%I A113470 #15 Jan 03 2020 05:31:27
%S A113470 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,
%T A113470 155,185,215,635,707,779,851,923,995,1067,1139,635,707,779,851,923,
%U A113470 995,1067,1139,1211,199,409,619,829,1039,1249,1459,1669,1879,2089,3841,3973
%N A113470 Triangle read by rows: n-th row is the smallest set of n numbers in arithmetic progression with the same number of divisors.
%C A113470 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.
%H A113470 OEIS wiki, <a href="https://oeis.org/wiki/Primes_in_arithmetic_progression">Primes in arithmetic progression</a>.
%F A113470 T(n,k) = A090547(n) + (k-1)*A090549(n). - _R. J. Mathar_, May 11 2007
%e A113470 From _M. F. Hasler_, Jan 02 2020: (Start)
%e A113470 The triangle starts
%e A113470     n | row n
%e A113470    ---+------------
%e A113470     1 |    1,
%e A113470     2 |    2,    3,
%e A113470     3 |    3,    5,    7,
%e A113470     4 |    5,   11,   17,   23,
%e A113470     5 |    5,   11,   17,   23,   29,
%e A113470     6 |    7,   37,   67,   97,  127,  157,
%e A113470     7 |   35,   65,   95,  125,  155,  185,  215,
%e A113470     8 |  635,  707,  779,  851,  923,  995, 1067, 1139,
%e A113470     9 |  635,  707,  779,  851,  923,  995, 1067, 1139, 1211,
%e A113470    10 |  199,  409,  619,  829, 1039, 1249, 1459, 1669, 1879, 2089,
%e A113470    11 | 3841, 3973,  ...
%e A113470 Most rows so far consist of primes with 2 divisors, rows 7, 8, 9 and 11 have squarefree semiprimes with 4 divisors.
%e A113470 Row 10 is A033168; also row 10 of A086786, A133276 and A133277. (End)
%Y A113470 Cf. A086786, A090547, A090548, A090549.
%K A113470 nonn,tabl
%O A113470 1,2
%A A113470 _David Wasserman_, Jan 08 2006