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

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

Offset: 1

Author

Amarnath Murthy, May 07 2003

Keywords

• nonn
• tabl

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.

Examples

			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.
		

Links

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

Crossrefs

Cf. A083789, A083790, A083791.

Extensions

Corrected and extended by Ray Chandler, Aug 17 2003