A284268 Sum of coefficients > 1 in the Stern polynomial B(2n+1,x): a(n) = A275812(A277324(n)).

0, 0, 2, 0, 2, 3, 4, 0, 2, 6, 7, 5, 5, 6, 6, 0, 2, 8, 9, 9, 10, 11, 11, 7, 7, 11, 12, 9, 8, 9, 8, 0, 2, 10, 12, 11, 13, 17, 16, 12, 13, 18, 20, 16, 15, 17, 15, 9, 9, 15, 17, 16, 17, 19, 18, 12, 11, 16, 17, 13, 11, 12, 10, 0, 2, 12, 15, 14, 17, 22, 21, 15, 17, 25, 27, 24, 23, 26, 22, 15, 16, 24, 29, 26, 28, 32, 30, 21, 20, 28, 30, 24, 21, 23, 19, 11, 11, 19

Offset

0,3

Comments

Sum of terms larger than one on row 2n+1 of table A125184.

Links

Antti Karttunen, Table of n, a(n) for n = 0..8192

Formula

a(n) = A284272((2*n)+1).

a(n) = A275812(A277324(n)).

Other identities. For all n >= 0:

A007306(1+n) = A284267(n) + a(n).

Mathematica

A003961[p_?PrimeQ] := A003961[p] = Prime[ PrimePi[p] + 1]; A003961[1] = 1; A003961[n_] := A003961[n] = Times @@ (A003961[First[#]] ^ Last[#] & ) /@ FactorInteger[n] (* after 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]]]; A275812[n_]:= PrimeOmega[n] - If[n<2, 0, Count[Transpose[FactorInteger[n]][[2]], 1]]; Table[A275812[A260443[2n + 1]], {n, 0, 150}] (* Indranil Ghosh, Mar 28 2017 *)

Prog

(PARI) A284268(n) = A284272(n+n+1); \\ Other code as in A284272.
(Scheme)
(define (A284268 n) (A284272 (+ n n 1)))
(define (A284268 n) (A275812 (A277324 n)))

Crossrefs

Cf. A007306, A125184, A260443, A275812, A277324, A284267.

Odd bisection of A284272.

Sequence in context: A261217 A352957 A245230 * A063180 A263624 A141693

Adjacent sequences: A284265 A284266 A284267 * A284269 A284270 A284271

Keyword

nonn

Author

Antti Karttunen, Mar 25 2017

Status

approved