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A376557 Triangle read by rows: the n-th row gives the least sequence of n consecutive numbers with the same number of divisors.

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%I A376557 #15 Sep 29 2024 08:56:26
%S A376557 1,2,3,33,34,35,242,243,244,245,11605,11606,11607,11608,11609,28374,
%T A376557 28375,28376,28377,28378,28379,171893,171894,171895,171896,171897,
%U A376557 171898,171899,1043710445721,1043710445722,1043710445723,1043710445724,1043710445725,1043710445726,1043710445727,1043710445728
%N A376557 Triangle read by rows: the n-th row gives the least sequence of n consecutive numbers with the same number of divisors.
%C A376557 Inspired by the 4th row given by Guy.
%D A376557 R. K. Guy, Unsolved Problems in Number Theory, Springer, 1st edition, 1981. See section B18.
%e A376557 The triangle begins as:
%e A376557        1;
%e A376557        2,      3;
%e A376557       33,     34,     35;
%e A376557      242,    243,    244,    245;
%e A376557    11605,  11606,  11607,  11608,  11609;
%e A376557    28374,  28375,  28376,  28377,  28378,  28379;
%e A376557   171893, 171894, 171895, 171896, 171897, 171898, 171899;
%e A376557   ...
%t A376557 row[n_]:=Module[{}, k=1; nd=DivisorSigma[0,k]; While[Product[Boole[DivisorSigma[0,k+i]==nd], {i, n-1}]!=1, k++; nd=DivisorSigma[0,k]]; Table[i+k, {i, 0, n-1}]]; Array[row, 7]//Flatten
%Y A376557 Cf. A000005, A006558 (1st column), A019273 (right diagonal), A039665.
%K A376557 nonn,tabl
%O A376557 1,2
%A A376557 _Stefano Spezia_, Sep 28 2024