

A094950


Number of integer coefficients in nth Bernoulli polynomial (including zeros).


1



1, 1, 2, 2, 4, 3, 4, 4, 5, 7, 8, 8, 10, 8, 8, 8, 12, 9, 14, 12, 13, 15, 14, 12, 17, 16, 14, 18, 22, 21, 16, 16, 24, 24, 24, 27, 34, 28, 26, 26, 30, 25, 30, 28, 28, 32, 26, 26, 35, 32, 31, 37, 33, 27, 36, 39, 45, 46, 39, 39, 43, 40, 32, 32, 47, 51, 54, 47, 45, 49, 51
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OFFSET

0,3


LINKS

Robert Israel, Table of n, a(n) for n = 0..5160


EXAMPLE

B(5,x) = x^5  5/2*x^4 + 5/3*x^3 + 0*x^2  1/6*x + 0 hence a(5) = 3


MAPLE

f:= proc(n) local B;
B:= bernoulli(n, x);
nops(select(t > coeff(B, x, t)::integer, [$0..degree(B)]))
end proc:
map(f, [$0..100]); # Robert Israel, Aug 28 2018


MATHEMATICA

a[n_] := Select[CoefficientList[BernoulliB[n, x], x], IntegerQ] // Length;
a /@ Range[0, 100] (* JeanFrançois Alcover, Aug 26 2020 *)


PROG

(PARI) B(n, x)=sum(i=0, n, binomial(n, i)*bernfrac(i)*x^(ni)); a(n)=sum(i=0, n, if(frac(polcoeff(B(n, x), i)), 0, 1))


CROSSREFS

Sequence in context: A087808 A217754 A319397 * A087874 A166267 A117484
Adjacent sequences: A094947 A094948 A094949 * A094951 A094952 A094953


KEYWORD

nonn


AUTHOR

Benoit Cloitre, Jun 19 2004


STATUS

approved



