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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
OFFSET
0,4
COMMENTS
Number of 1's on row n of table A125184.
LINKS
FORMULA
a(n) = A056169(A260443(n)).
Other identities and observations. For all n >= 0:
A002487(n) = a(n) + A284272(n).
a(n) <= A277700(n).
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
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
(Scheme) (define (A284271 n) (A056169 (A260443 n)))
CROSSREFS
Cf. A002487, A056169, A125184, A260443, A277700, A284272, A284267 (odd bisection).
Sequence in context: A109671 A141289 A368878 * A241915 A301891 A332089
KEYWORD
nonn
AUTHOR
Antti Karttunen, Mar 25 2017
STATUS
approved