A374113 - OEIS

A374113

a(n) = 1 if A113177(n) and A276085(n) are both even, otherwise 0, where A113177 and A276085 are fully additive with a(p) = Fibonacci(p) and a(p) = p#/p, respectively.

1, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1

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OFFSET

COMMENTS

a(n) = 1 if the 2-adic valuation of n is even, and the number of its prime factors (with multiplicity, A001222) and its 3-adic valuation (A007949) have the same parity, otherwise 0.

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..100000

Index entries for characteristic functions

FORMULA

a(n) = A035263(n) * A373585(n).

a(n) = A059841(A374112(n)).

PROG

(PARI)

A113177(n) = if(n<=1, 0, my(f=factor(n)); sum(i=1, #f~, f[i, 2]*fibonacci(f[i, 1])));

A276085(n) = { my(f=factor(n)); sum(k=1, #f~, f[k, 2]*prod(i=1, primepi(f[k, 1]-1), prime(i))); };

A374113(n) = (!(A113177(n)%2) && !(A276085(n)%2));

(PARI) A374113(n) = (!(valuation(n, 2)%2) && !((bigomega(n)-valuation(n, 3))%2));

CROSSREFS

Characteristic function of A374114, whose complement A374115 gives the indices of 0's.

Cf. A001222, A007949, A035263, A113177, A059841, A276085, A373585, A374112.

Sequence in context: A185295 A214295 A145377 * A374107 A373585 A246260

Adjacent sequences: A374110 A374111 A374112 * A374114 A374115 A374116

KEYWORD

nonn

AUTHOR

Antti Karttunen, Jun 29 2024

STATUS

approved