A248937 - OEIS

%I #20 Oct 25 2014 22:57:01

%S 1,2,3,4,5,3,7,4,6,5,11,4,13,8,5,6,17,8,19,5,12,14,23,4,10,14,33,8,29,

%T 5,31,8,12,17,7,8,37,22,13,5,41,22,43,12,6,23,47,27,14,14,21,13,53,33,

%U 15,8,21,29,59,5,61,32,7,8,15,14,67,17,23,8,71,8,73

%N Fermi-Dirac analog of the Kempner numbers (A002034) (see comment).

%C a(n) is the smallest number m such that if the product of distinct terms q_1,...,q_k of A050376 equals n, then {q_1,...,q_k} is a subset of the set of distinct terms of A050376, the product of which equals m! Note that, in Fermi-Dirac arithmetic 1 corresponds to the empty set of Fermi-Dirac primes (A050376). a(n) differs from A002034(n) for n=14,18,21,22,26,27,28,33,36,38,42,...

%C Note that A002034(n)<=n, while a(n) can exceed n. The first example is a(27)=33. Are there other n's for which a(n)>n?

%C There are no others up to n=5000. - _Peter J. C. Moses_, Oct 21 2014

%H Peter J. C. Moses, <a href="/A248937/b248937.txt">Table of n, a(n) for n = 1..5000</a>

%F For prime p, a(p)=p; a(n)>=A002034(n).

%e Let n = 14 = 2*7. It is clear that a(n)>=7, but the Fermi-Dirac factorization of 7! is 7!=5*7*9*16. It does not contain 2, while 8!=2*4*5*7*9*16 does contain both 2 and 7. So a(14)=8.

%Y Cf. A002034, A050376.

%K nonn

%O 1,2

%A _Vladimir Shevelev_, Oct 17 2014

%E More terms from _Peter J. C. Moses_, Oct 17 2014