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

1,2

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

Links

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

Formula

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

Example

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.

Crossrefs

Cf. A002034, A050376.

Sequence in context: A077004 A064760 A002034 * A088491 A353172 A140271

Adjacent sequences: A248934 A248935 A248936 * A248938 A248939 A248940

Keyword

nonn

Author

Vladimir Shevelev, Oct 17 2014

Extensions

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

Status

approved