|
|
A284271
|
|
Number of terms with coefficient 1 in the Stern polynomial B(n,x): a(n) = A056169(A260443(n)).
|
|
3
|
|
|
0, 1, 1, 2, 1, 1, 2, 3, 1, 2, 1, 2, 2, 1, 3, 4, 1, 3, 2, 1, 1, 1, 2, 2, 2, 2, 1, 2, 3, 1, 4, 5, 1, 4, 3, 1, 2, 2, 1, 1, 1, 1, 1, 2, 2, 1, 2, 2, 2, 2, 2, 1, 1, 1, 2, 2, 3, 2, 1, 2, 4, 1, 5, 6, 1, 5, 4, 1, 3, 2, 1, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 1, 2, 2, 1, 2, 2, 2, 2, 2, 1, 2, 2, 1, 1, 1, 1, 1, 2, 2, 1, 2, 2, 3, 2, 2, 1, 1, 1, 2, 2, 4
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,4
|
|
COMMENTS
|
Number of 1's on row n of table A125184.
|
|
LINKS
|
|
|
FORMULA
|
Other identities and observations. For all n >= 0:
|
|
MATHEMATICA
|
A003961[p_?PrimeQ] := A003961[p] = Prime[ PrimePi[p] + 1]; A003961[1] = 1; A003961[n_] := A003961[n] = Times @@ ( A003961[First[#]] ^ Last[#] & ) /@ FactorInteger[n](* Jean-François Alcover, Dec 01 2011 *); A260443[n_]:= If[n<2, n + 1, If[EvenQ[n], A003961[A260443[n/2]], A260443[(n - 1)/2] * A260443[(n + 1)/2]]]; a[n_]:= If[n<2, 0, Count[Transpose[FactorInteger[n]][[2]], 1]]; Table[a[A260443[n]], {n, 0, 150}] (* Indranil Ghosh, Mar 28 2017 *)
|
|
PROG
|
(PARI)
A003961(n) = my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); \\ From Michel Marcus
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|