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A354918
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a(n) = A344005(n) mod 2, where A344005(n) is the smallest positive m such that n divides the oblong number m*(m+1).
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6
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1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0
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internal format)
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OFFSET
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1
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LINKS
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FORMULA
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PROG
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(PARI) A354918(n) = for(m=1, oo, if((m*(m+1))%n==0, return(m%2)));
(Python 3.8+)
from itertools import combinations
from math import prod
from sympy import factorint
from sympy.ntheory.modular import crt
if n == 1:
return 1
plist = tuple(p**q for p, q in factorint(n).items())
return (n-1 if len(plist) == 1 else int(min(min(crt((m, n//m), (0, -1))[0], crt((n//m, m), (0, -1))[0]) for m in (prod(d) for l in range(1, len(plist)//2+1) for d in combinations(plist, l))))) & 1 # Chai Wah Wu, Jun 12 2022
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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