A085929 Smaller of two consecutive numbers with the same prime signature not occurring earlier.

2, 14, 44, 135, 230, 819, 2295, 2511, 5264, 7314, 8991, 11780, 21735, 23275, 29888, 37664, 41624, 156735, 223244, 257499, 378014, 458864, 477224, 916352, 1241954, 2808351, 3341624, 4122495, 4388175, 4402431, 5430375, 5475519, 6481475

Offset

1,1

Comments

The order of the exponents in the prime factorization is not significant (compare A091405).

Conjecture: (1) The sequence is infinite. (2) For every prime signature other than perfect powers, there exists a number k such that k+1 also has the same prime signature.

Up to at least 3*10^8, all numbers in this sequence have signatures with some prime to power 1 (for example, p^2*q^3 does not appear), casting some doubt on the second conjecture. - Joseph Myers, Feb 24 2004

Links

Amiram Eldar, Table of n, a(n) for n = 1..112

Example

2 and 3 both are prime, 14 and 15 both are of the type p*q and 44 and 45 both are of the prime signature p^2*q. All prime signatures occur only once.

Crossrefs

Cf. A025487, A091405.

Sequence in context: A075036 A212902 A091405 * A231247 A318764 A036659

Adjacent sequences: A085926 A085927 A085928 * A085930 A085931 A085932

Keyword

nonn

Author

Amarnath Murthy, Jul 14 2003

Extensions

More terms from Joseph Myers, Feb 24 2004

Offset corrected by Amiram Eldar, Jul 23 2021

Status

approved