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A302776 a(1) = 1; for n>1, a(n) = n/(largest Fermi-Dirac factor of n). 6
1, 1, 1, 1, 1, 2, 1, 2, 1, 2, 1, 3, 1, 2, 3, 1, 1, 2, 1, 4, 3, 2, 1, 6, 1, 2, 3, 4, 1, 6, 1, 2, 3, 2, 5, 4, 1, 2, 3, 8, 1, 6, 1, 4, 5, 2, 1, 3, 1, 2, 3, 4, 1, 6, 5, 8, 3, 2, 1, 12, 1, 2, 7, 4, 5, 6, 1, 4, 3, 10, 1, 8, 1, 2, 3, 4, 7, 6, 1, 5, 1, 2, 1, 12, 5, 2, 3, 8, 1, 10, 7, 4, 3, 2, 5, 6, 1, 2, 9, 4, 1, 6, 1, 8, 15 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,6
COMMENTS
For n > 1, a(n) = the smallest positive number d such that n/d is a "Fermi-Dirac prime", a term of A050376.
LINKS
FORMULA
a(n) = n / A223491(n).
a(n) = A302023(A052126(A302024(n))).
MATHEMATICA
f[p_, e_] := p^(2^Floor[Log2[e]]); a[n_] := n / Max @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Nov 26 2020 *)
PROG
(PARI)
A209229(n) = (n && !bitand(n, n-1));
A302777(n) = A209229(isprimepower(n));
A302776(n) = if(1==n, n, fordiv(n, d, if(A302777(n/d), return(d))));
CROSSREFS
Cf. A084400 (gives the positions of 1's).
Cf. also A052126, A284600.
Sequence in context: A245661 A302789 A346089 * A366510 A366522 A345934
KEYWORD
nonn
AUTHOR
Antti Karttunen, Apr 13 2018
STATUS
approved

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Last modified March 28 13:42 EDT 2024. Contains 371254 sequences. (Running on oeis4.)