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Smaller of two consecutive numbers with the same prime signature not occurring earlier.
2

%I #10 Jul 23 2021 05:31:19

%S 2,14,44,135,230,819,2295,2511,5264,7314,8991,11780,21735,23275,29888,

%T 37664,41624,156735,223244,257499,378014,458864,477224,916352,1241954,

%U 2808351,3341624,4122495,4388175,4402431,5430375,5475519,6481475

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

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

%C 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.

%C 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

%H Amiram Eldar, <a href="/A085929/b085929.txt">Table of n, a(n) for n = 1..112</a>

%e 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.

%Y Cf. A025487, A091405.

%K nonn

%O 1,1

%A _Amarnath Murthy_, Jul 14 2003

%E More terms from _Joseph Myers_, Feb 24 2004

%E Offset corrected by _Amiram Eldar_, Jul 23 2021