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

1,3

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