A241289 Numbers n for which in the factorization of n! over distinct terms of A050376, the numbers of prime and nonprime terms are equal.

7, 8, 9, 13, 18, 22, 37, 57, 71

Offset

1,1

Comments

a(10), if it exists, should be more than 5000. Is a(9)=71 the last term of sequence? - Peter J. C. Moses, Apr 19 2014

One can prove that a(9)=71 indeed is the last term of this sequence. - Vladimir Shevelev, Apr 19 2014.

References

V. S. Shevelev, Multiplicative functions in the Fermi-Dirac arithmetic, Izvestia Vuzov of the North-Caucasus region, Nature sciences 4 (1996), 28-43 [Russian].

Links

Table of n, a(n) for n=1..9.

S. Litsyn and V. S. Shevelev, On factorization of integers with restrictions on the exponent, INTEGERS: Electronic Journal of Combinatorial Number Theory, 7 (2007), #A33, 1-36.

Example

7 is in the sequence, since 7! in the considered factorization is 5*7*9*16, and here we have 2 primes and 2 nonprimes.

Crossrefs

Cf. A177329, A177333, A177334, A240537, A240606, A240619, A240620, A240668, A240669, A240670, A240672, A240695, A240751, A240755, A240764, A240905, A240906, A241123, A241124, A241139, A241148.

Sequence in context: A297131 A289740 A289760 * A037369 A076599 A067197

Adjacent sequences: A241286 A241287 A241288 * A241290 A241291 A241292

Keyword

nonn,fini,full

Author

Vladimir Shevelev, Apr 18 2014

Extensions

Terms a(7) - a(9) from Peter J. C. Moses, Apr 19 2014

Status

approved