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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. 6

%I

%S 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 30,1804,1805,1806,1807,1808,1809,1810,1811,1968,1969,1970,1971,1972,

%U 1973,1974,1975,1976,8375,8376,8377,8378,8379,8380,8381,8382,8383,8384

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

%C 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 Giovanni Resta, <a href="/A083788/b083788.txt">Table of n, a(n) for n = 1..190</a>

%e 1;

%e 1,2;

%e 4,5,6;

%e 6,7,8,9;

%e 8,9,10,11,12;

%e 23,24,25,26,27,28;

%e 24,25,26,27,28,29,30;

%e 1804,1805,1806,1807,1808,1809,1810,1811;

%e 1968,1969,1970,1971,1972,1973,1974,1975,1976;

%e 8375,8376,8377,8378,8379,8380,8381,8382,8383,8384;

%e 53750,53751,53752,53753,53754,53755,53756,53757,53758,53759,53760;

%e ...

%e Row 4 contains 6,7,8 and 9 with prime signatures p*q,p,p^3,p^2 respectively.

%Y Cf. A083789, A083790, A083791.

%K nonn,tabl

%O 1,3

%A _Amarnath Murthy_, May 07 2003

%E Corrected and extended by _Ray Chandler_, Aug 17 2003

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Last modified November 27 09:19 EST 2021. Contains 349365 sequences. (Running on oeis4.)