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A367544
Euclid's triangle A217831 represented as decimal numbers.
6
0, 3, 2, 6, 10, 30, 34, 126, 170, 438, 650, 2046, 2210, 8190, 10794, 27030, 43690, 131070, 141474, 524286, 666250, 1781046, 2794154, 8388606, 9054370, 32472030, 44731050, 115043766, 176859690, 536870910, 545925250, 2147483646, 2863311530, 7358604726, 11453115050
OFFSET
0,2
COMMENTS
The decimal equivalents of A367547.
FORMULA
a(n) = Sum_{k=0..n} 2^k * |(n - k | k)|, where (a | b) denotes the Kronecker symbol.
a(n) = Sum_{k=0..n} [gcd(k, n) = 1] * 2^k, where [] is the Iverson bracket.
MAPLE
KS := (n, k) -> NumberTheory:-KroneckerSymbol(n, k):
A367544 := n -> local k; add(2^k * abs(KS(n - k, k)), k = 0..n):
seq(A367544(n), n = 0..34);
MATHEMATICA
A367544[n_]:=FromDigits[Boole[CoprimeQ[n, Range[0, n]]], 2];
Array[A367544, 50, 0] (* Paolo Xausa, Nov 24 2023 *)
PROG
(SageMath) # For Python include 'import math' for math.gcd.
def a(n):
cop = [int(gcd(i, n) == 1) for i in range(n + 1)]
return sum(p * 2^k for k, p in enumerate(cop))
print([a(n) for n in range(35)])
(PARI) a(n) = sum(k=0, n, 2^k*abs(kronecker(n-k, k))); \\ Michel Marcus, Nov 23 2023
(PARI) a(n) = fromdigits(vector(n+1, i, gcd(i-1, n)==1), 2); \\ Michel Marcus, Nov 24 2023
(Python)
from math import gcd
def A367544(n): return sum(1<<k for k in range(n+1) if gcd(n, k)==1) # Chai Wah Wu, Nov 24 2023
KEYWORD
nonn,base
AUTHOR
Peter Luschny, Nov 22 2023
STATUS
approved