

A083788


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


6



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, 30, 1804, 1805, 1806, 1807, 1808, 1809, 1810, 1811, 1968, 1969, 1970, 1971, 1972, 1973, 1974, 1975, 1976, 8375, 8376, 8377, 8378, 8379, 8380, 8381, 8382, 8383, 8384
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OFFSET

1,3


COMMENTS

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.


LINKS

Giovanni Resta, Table of n, a(n) for n = 1..190


EXAMPLE

1;
1,2;
4,5,6;
6,7,8,9;
8,9,10,11,12;
23,24,25,26,27,28;
24,25,26,27,28,29,30;
1804,1805,1806,1807,1808,1809,1810,1811;
1968,1969,1970,1971,1972,1973,1974,1975,1976;
8375,8376,8377,8378,8379,8380,8381,8382,8383,8384;
53750,53751,53752,53753,53754,53755,53756,53757,53758,53759,53760;
...
Row 4 contains 6,7,8 and 9 with prime signatures p*q,p,p^3,p^2 respectively.


CROSSREFS

Cf. A083789, A083790, A083791.
Sequence in context: A291768 A059583 A086370 * A058317 A278761 A287076
Adjacent sequences: A083785 A083786 A083787 * A083789 A083790 A083791


KEYWORD

nonn,tabl


AUTHOR

Amarnath Murthy, May 07 2003


EXTENSIONS

Corrected and extended by Ray Chandler, Aug 17 2003


STATUS

approved



