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A284264 a(n) = A001222(A283983(n)). 4
0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 2, 0, 0, 0, 1, 1, 2, 1, 3, 1, 2, 0, 2, 2, 2, 0, 3, 0, 0, 0, 1, 1, 3, 1, 4, 2, 4, 1, 5, 3, 5, 1, 5, 2, 3, 0, 3, 2, 4, 2, 5, 2, 4, 0, 3, 3, 3, 0, 4, 0, 0, 0, 1, 1, 4, 1, 5, 3, 5, 1, 6, 4, 8, 2, 7, 4, 5, 1, 6, 5, 8, 3, 10, 5, 7, 1, 7, 5, 8, 2, 7, 3, 4, 0, 4, 3, 6, 2, 8, 4, 7, 2, 8, 5, 9, 2, 8, 4, 5, 0, 5, 3, 6, 3, 7, 3, 6, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,14

COMMENTS

a(n) = Sum_{c} floor(c/2), where c ranges over each coefficient of terms c * x^k in the Stern polynomial B(n,x), thus sum of the halved terms (for odd terms floored down) on row n of table A125184.

LINKS

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

Index entries for sequences related to binary expansion of n

FORMULA

a(n) = A001222(A283983(n)).

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

a(2n) = a(n).

a(n) = (1/2) * (A002487(n) - A277700(n)).

2*a(n) <= A284272(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-Fran├žois 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]]]; A000188[n_]:= Sum[Boole[Mod[i^2, n] == 0], {i, n}]; Table[PrimeOmega[A000188[A260443[n]]], {n, 0, 120}] (* Indranil Ghosh, Mar 28 2017 *)

PROG

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.

A000188(n) = core(n, 1)[2]; \\ This function from Michel Marcus, Feb 27 2013

A283983(n) = A000188(A260443(n));

A284264(n) = bigomega(A283983(n));

(Scheme) (define (A284264 n) (/ (- (A002487 n) (A277700 n)) 2))

CROSSREFS

Cf. A000188, A002487, A001222, A125184, A260443, A277700, A283983, A284265 (odd bisection), A284272.

Cf. A023758 (gives the positions of zeros).

Sequence in context: A091890 A029431 A091492 * A273302 A025086 A035699

Adjacent sequences:  A284261 A284262 A284263 * A284265 A284266 A284267

KEYWORD

nonn

AUTHOR

Antti Karttunen, Mar 25 2017

STATUS

approved

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Last modified March 18 20:24 EDT 2019. Contains 321294 sequences. (Running on oeis4.)