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A353816
a(n) = 1 if n is a number of the form x^2 + xy + y^2, otherwise 0.
4
1, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0
OFFSET
0
COMMENTS
a(n) = 1 iff in the prime factorization of n, all primes == 2 (mod 3) occur to even powers.
FORMULA
a(n) = [A088534(n) > 0], where [ ] is the Iverson bracket.
a(n) >= A353815(n).
Multiplicative with a(p^e) = 0 if p == 2 (mod 3) and e is odd, and a(p^e) = 1 in all other cases. - Antti Karttunen, Jul 04 2024
PROG
(PARI) A353816(n) = if(!n, 1, my(f=factor(n), flag=1); for(i=1, #f~, if(Mod(f[i, 1], 3)==2 && Mod(f[i, 2], 2)==1, flag=0)); (flag)); \\ After function isA003136 in A003136.
(PARI) A353816(n) = if(!n, 1, my(f=factor(n)); prod(i=1, #f~, (2!=(f[i, 1]%3) || (1+f[i, 2])%2))); \\ Antti Karttunen, Jul 04 2024
CROSSREFS
Characteristic function of A003136.
Sequence in context: A278513 A134842 A167753 * A141727 A298952 A123594
KEYWORD
nonn,mult
AUTHOR
Antti Karttunen, May 15 2022
EXTENSIONS
Keyword:mult added by Antti Karttunen, Jul 04 2024
STATUS
approved