A367544 - OEIS

%I #26 Nov 24 2023 12:37:53

%S 0,3,2,6,10,30,34,126,170,438,650,2046,2210,8190,10794,27030,43690,

%T 131070,141474,524286,666250,1781046,2794154,8388606,9054370,32472030,

%U 44731050,115043766,176859690,536870910,545925250,2147483646,2863311530,7358604726,11453115050

%N Euclid's triangle A217831 represented as decimal numbers.

%C The decimal equivalents of A367547.

%F a(n) = Sum_{k=0..n} 2^k * |(n - k | k)|, where (a | b) denotes the Kronecker symbol.

%F a(n) = Sum_{k=0..n} [gcd(k, n) = 1] * 2^k, where [] is the Iverson bracket.

%p KS := (n, k) -> NumberTheory:-KroneckerSymbol(n, k):

%p A367544 := n -> local k; add(2^k * abs(KS(n - k, k)), k = 0..n):

%p seq(A367544(n), n = 0..34);

%t A367544[n_]:=FromDigits[Boole[CoprimeQ[n,Range[0,n]]],2];

%t Array[A367544,50,0] (* _Paolo Xausa_, Nov 24 2023 *)

%o (SageMath)  # For Python include 'import math' for math.gcd.

%o def a(n):

%o     cop = [int(gcd(i, n) == 1) for i in range(n + 1)]

%o     return sum(p * 2^k for k, p in enumerate(cop))

%o print([a(n) for n in range(35)])

%o (PARI) a(n) = sum(k=0, n, 2^k*abs(kronecker(n-k, k))); \\ _Michel Marcus_, Nov 23 2023

%o (PARI) a(n) = fromdigits(vector(n+1, i, gcd(i-1, n)==1), 2); \\ _Michel Marcus_, Nov 24 2023

%o (Python)

%o from math import gcd

%o def A367544(n): return sum(1<<k for k in range(n+1) if gcd(n,k)==1) # _Chai Wah Wu_, Nov 24 2023

%Y Cf. A217831, A000010, A023896, A055034, A349136, A367545, A367546, A367547.

%K nonn,base

%O 0,2

%A _Peter Luschny_, Nov 22 2023