|
|
A302792
|
|
a(1) = 1; for n>1, a(n) = n/(smallest Fermi-Dirac factor of n).
|
|
6
|
|
|
1, 1, 1, 1, 1, 3, 1, 4, 1, 5, 1, 4, 1, 7, 5, 1, 1, 9, 1, 5, 7, 11, 1, 12, 1, 13, 9, 7, 1, 15, 1, 16, 11, 17, 7, 9, 1, 19, 13, 20, 1, 21, 1, 11, 9, 23, 1, 16, 1, 25, 17, 13, 1, 27, 11, 28, 19, 29, 1, 20, 1, 31, 9, 16, 13, 33, 1, 17, 23, 35, 1, 36, 1, 37, 25, 19, 11, 39, 1, 16, 1, 41, 1, 28, 17, 43, 29, 44, 1, 45, 13, 23, 31, 47, 19, 48, 1
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,6
|
|
COMMENTS
|
The positive integers that are absent from this sequence are A036554, integers that have 2 as a Fermi-Dirac factor. - Peter Munn, Apr 23 2018
a(n) is the largest aliquot infinitary divisor of n, for n > 1 (cf. A077609). - Amiram Eldar, Nov 19 2022
|
|
LINKS
|
|
|
FORMULA
|
|
|
MATHEMATICA
|
f[p_, e_] := p^(2^IntegerExponent[e, 2]); a[n_] := n / Min @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Nov 27 2020 *)
|
|
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); };
(PARI) a(n) = {if(n==1, 1, my(f = factor(n)); for(i=1, #f~, f[i, 1] = f[i, 1]^(1<<valuation(f[i, 2], 2))); n/vecmin(f[, 1])); } \\ Amiram Eldar, Nov 19 2022
|
|
CROSSREFS
|
Cf. A084400 (gives the positions of 1's).
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|