A248937 Fermi-Dirac analog of the Kempner numbers (A002034) (see comment).

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

Offset: 1

Author

Vladimir Shevelev, Oct 17 2014

Keywords

• nonn

Comments

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,...

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?

There are no others up to n=5000. - Peter J. C. Moses, Oct 21 2014

Examples

			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.
		

Links

• Peter J. C. Moses, Table of n, a(n) for n = 1..5000

Crossrefs

Cf. A002034, A050376.

Formula

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

Extensions

More terms from Peter J. C. Moses, Oct 17 2014