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A083788 Triangle read by rows, in which n-th row contains smallest set of n consecutive numbers with distinct prime signatures.

%I A083788 #9 Jul 14 2015 04:17:24
%S A083788 1,1,2,4,5,6,6,7,8,9,8,9,10,11,12,23,24,25,26,27,28,24,25,26,27,28,29,
%T A083788 30,1804,1805,1806,1807,1808,1809,1810,1811,1968,1969,1970,1971,1972,
%U A083788 1973,1974,1975,1976,8375,8376,8377,8378,8379,8380,8381,8382,8383,8384
%N A083788 Triangle read by rows, in which n-th row contains smallest set of n consecutive numbers with distinct prime signatures.
%C A083788 Question: Given n with a prime signature say p^a*q^b*r^c... find a tight upper limit m such that there exists a number k, n < k < m with the same prime signature.
%H A083788 Giovanni Resta, <a href="/A083788/b083788.txt">Table of n, a(n) for n = 1..190</a>
%e A083788 1;
%e A083788 1,2;
%e A083788 4,5,6;
%e A083788 6,7,8,9;
%e A083788 8,9,10,11,12;
%e A083788 23,24,25,26,27,28;
%e A083788 24,25,26,27,28,29,30;
%e A083788 1804,1805,1806,1807,1808,1809,1810,1811;
%e A083788 1968,1969,1970,1971,1972,1973,1974,1975,1976;
%e A083788 8375,8376,8377,8378,8379,8380,8381,8382,8383,8384;
%e A083788 53750,53751,53752,53753,53754,53755,53756,53757,53758,53759,53760;
%e A083788 ...
%e A083788 Row 4 contains 6,7,8 and 9 with prime signatures p*q,p,p^3,p^2 respectively.
%Y A083788 Cf. A083789, A083790, A083791.
%K A083788 nonn,tabl
%O A083788 1,3
%A A083788 _Amarnath Murthy_, May 07 2003
%E A083788 Corrected and extended by _Ray Chandler_, Aug 17 2003