A284272 Sum of coefficients > 1 in the Stern polynomial B(n,x): a(n) = A275812(A260443(n)).

0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 2, 3, 0, 4, 0, 0, 0, 2, 2, 6, 2, 7, 3, 5, 0, 5, 4, 6, 0, 6, 0, 0, 0, 2, 2, 8, 2, 9, 6, 9, 2, 10, 7, 11, 3, 11, 5, 7, 0, 7, 5, 11, 4, 12, 6, 9, 0, 8, 6, 9, 0, 8, 0, 0, 0, 2, 2, 10, 2, 12, 8, 11, 2, 13, 9, 17, 6, 16, 9, 12, 2, 13, 10, 18, 7, 20, 11, 16, 3, 15, 11, 17, 5, 15, 7, 9, 0, 9, 7, 15, 5, 17, 11, 16, 4, 17, 12, 19, 6, 18, 9

Offset: 0

Author

Antti Karttunen, Mar 25 2017

Keywords

• nonn

Comments

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

Links

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

Crossrefs

Cf. A002487, A125184, A260443, A275812, A284264, A284271, A284268 (odd bisection).

Programs

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[n]], {n, 0, 150}] (* Indranil Ghosh, Mar 28 2017 *)

PARI

A003961(n) = my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); \\ From Michel Marcus
A260443(n) = if(n<2, n+1, if(n%2, A260443(n\2)*A260443(n\2+1), A003961(A260443(n\2)))); \\ Cf. Charles R Greathouse IV's code for "ps" in A186891 and A277013.
A056169(n) = { my(f=factor(n)[, 2]); sum(i=1, #f, f[i]==1); }; \\ This function from Charles R Greathouse IV, Apr 29 2015
A275812(n) = bigomega(n) - A056169(n);
A284272(n) = A275812(A260443(n));

Scheme

(define (A284272 n) (A275812 (A260443 n)))

Formula

a(n) = A275812(A260443(n)).

Other identities and observations. For all n >= 0:

A002487(n) = A284271(n) + a(n).

a(n) >= 2*A284264(n).