A083789 -id:A083789 - cp's OEIS frontend

A086562 Duplicate of A083789.

1, 2, 6, 9, 12, 28, 30, 1811, 1976, 8384, 53760, 243875, 639336, 41381633, 102621357

Offset: 1

dead

A083790 Smallest start of n consecutive numbers with distinct prime signatures.

1, 1, 4, 6, 8, 23, 24, 1804, 1968, 8375, 53750, 243864, 639324, 41381620, 102621343, 7802708736, 7802708736, 178874468615, 1133934949368

Offset: 1

Amarnath Murthy, May 07 2003

a(16) > 750000000. - Ray Chandler, Aug 21 2003
a(16) > 6.646*10^9. - David Wasserman, Jan 08 2006
a(18) > 10^11. - Donovan Johnson, Oct 24 2009
a(20) > 10^13. - Giovanni Resta, Jul 13 2015

A124058 gives another version of the same sequence.
First column of A083788.
Cf. A083789, A083791, A034173.

Corrected and extended by Ray Chandler, Aug 17 2003
More terms from Ray Chandler, Aug 21 2003
a(16)-a(17) from Donovan Johnson, Oct 24 2009
a(18)-a(19) from Giovanni Resta, Jul 13 2015
New name from Jon E. Schoenfield, Nov 17 2022

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

Original entry on oeis.org

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

Amarnath Murthy, May 07 2003

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.

			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.

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

Cf. A083789, A083790, A083791.

Corrected and extended by Ray Chandler, Aug 17 2003

A083791 Prime signatures pertaining to A083788.

Original entry on oeis.org

1, 1, 2, 4, 2, 6, 6, 2, 8, 4, 8, 4, 6, 2, 12, 2, 24, 4, 6, 8, 12, 24, 4, 6, 8, 12, 2, 30, 60, 12, 210, 6, 48, 24, 30, 2, 240, 6, 30, 24, 60, 2, 210, 12, 120, 24, 120, 2, 30, 180, 60, 12, 210, 6, 192, 240, 210, 24, 12, 420, 30, 60, 120, 6, 2, 53760

Offset: 1

Amarnath Murthy, May 07 2003

			a(n) = k where k is the smallest number with the same prime signature as that of A083788(n).
1;
1,2;
4,2,6;
6,2,8,4;
8,4,6,2,12;
2,24,4,6,8,12;
24,4,6,8,12,2,30;
60,12,210,6,48,24,30,2;
240,6,30,24,60,2,210,12,120;
24,120,2,30,180,60,12,210,6,192;
240,210,24,12,420,30,60,120,6,2,53760;

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

Cf. A083788, A083789, A083790.

Corrected and extended by Ray Chandler, Aug 17 2003

cp's OEIS Frontend

A086562 Duplicate of A083789.

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A083790 Smallest start of n consecutive numbers with distinct prime signatures.

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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.

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A083791 Prime signatures pertaining to A083788.

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