OFFSET
1,4
COMMENTS
First differs from A335428 at n = 36. Differs from A050377, A344417 and A347437 at n = 1 and then at n = 36.
In the unique factorization of n in terms of distinct "Fermi-Dirac primes", n is represented as a product of prime powers (A246655) whose exponents are powers of 2 (A000079). a(n) is the maximal exponent of these prime powers (and not the maximal exponent of the exponents that are powers of 2). Thus, a(n) is a power of 2 for n >= 2.
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
Wikipedia, Fermi-Dirac prime.
FORMULA
EXAMPLE
For n = 972 = 2^2 * 3^5, the unique factorization of 972 in terms of distinct "Fermi-Dirac primes" is 2^(2^1) * 3^(2^0) * 3^(2^2). Therefore, a(972) = 2^2 = 4.
MATHEMATICA
a[n_] := 2^Floor[Log2[Max[FactorInteger[n][[;; , 2]]]]]; a[1] = 0; Array[a, 100]
PROG
(PARI) a(n) = if(n > 1, 2^exponent(vecmax(factor(n)[, 2])), 0);
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Amiram Eldar, Jan 05 2024
STATUS
approved