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A209198 a(n) = 1 if n not == 2 (mod 4) and relatively prime to 63 otherwise 0. 2
1, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..5000

FORMULA

G.f.: B(x) - B(x^7) - B(x^9) + B(x^63) where B(x) = (x + x^3 + x^4) / (1 - x^4).

a(n) is multiplicative with a(2^e) = 1 if e!=1, a(3^e) = 1 if e<2, a(7^e) = 0^e, a(p^e) = 1 otherwise.

a(n) = a(n + 252) = a(-n), a(4*n + 2) = a(7*n) = a(9*n) = 0 for all n in Z.

Euler transform is A119952.

EXAMPLE

G.f. = x + x^3 + x^4 + x^5 + x^8 + x^11 + x^12 + x^13 + x^15 + x^16 + x^17 + ...

MATHEMATICA

B[x_]:= (x + x^3 + x^4)/(1 - x^4); CoefficientList[Series[B[x] - B[x^7] - B[x^9] + B[x^63], {x, 0, 50}], x] (* G. C. Greubel, Aug 11 2018 *)

PROG

(PARI) {a(n) = my(A, p, e); n = abs(n); if( n<1, 0, A = factor(n); prod( k=1, matsize(A)[1], [p, e] = A[k, ]; if( p==2, e>1, p==3, e<2,  p==7, 0, 1)))};

(PARI) {a(n) = b(n) - b(n/7) - b(n/9) + b(n/63)}; {b(n) = if( n == round(n), n%4 != 2, 0)};

(PARI) {a(n) = n%4!=2 && n%7!=0 && n%9!=0};

CROSSREFS

Cf. A119952.

Sequence in context: A230298 A000480 A118251 * A282343 A099076 A282339

Adjacent sequences:  A209195 A209196 A209197 * A209199 A209200 A209201

KEYWORD

nonn,mult

AUTHOR

Michael Somos, Mar 05 2012

STATUS

approved

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Last modified March 26 10:18 EDT 2019. Contains 321491 sequences. (Running on oeis4.)