|
|
A302786
|
|
Index of the smallest Fermi-Dirac factor of n, a(1) = 0 by convention: a(n) = A302778(A223490(n)).
|
|
8
|
|
|
0, 1, 2, 3, 4, 1, 5, 1, 6, 1, 7, 2, 8, 1, 2, 9, 10, 1, 11, 3, 2, 1, 12, 1, 13, 1, 2, 3, 14, 1, 15, 1, 2, 1, 4, 3, 16, 1, 2, 1, 17, 1, 18, 3, 4, 1, 19, 2, 20, 1, 2, 3, 21, 1, 4, 1, 2, 1, 22, 2, 23, 1, 5, 3, 4, 1, 24, 3, 2, 1, 25, 1, 26, 1, 2, 3, 5, 1, 27, 4, 28, 1, 29, 2, 4, 1, 2, 1, 30, 1, 5, 3, 2, 1, 4, 1, 31, 1, 6, 3, 32, 1, 33, 1, 2
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,3
|
|
LINKS
|
|
|
FORMULA
|
|
|
MATHEMATICA
|
nn = 105; t = {}; k = 1;
While[lim = nn^(1/k); lim > 2,
t = Join[t, Prime[Range[PrimePi[lim]]]^k]; k = 2 k];
A223490[n_] := Table[{p, e} = pe; p^(2^IntegerExponent[e, 2]), {pe, FactorInteger[n]}] // Min;
|
|
PROG
|
(PARI)
up_to = 65537;
v050376 = vector(up_to);
ispow2(n) = (n && !bitand(n, n-1));
i = 0; for(n=1, oo, if(ispow2(isprimepower(n)), i++; v050376[i] = n); if(i == up_to, break));
A052331(n) = { my(s=0, e); while(n > 1, fordiv(n, d, if(((n/d)>1)&&ispow2(isprimepower(n/d)), e = vecsearch(v050376, n/d); if(!e, print("v050376 too short!"); return(1/0)); s += 2^(e-1); n = d; break))); (s); };
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|