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A354993
a(n) = 1 if A344005(d) < A344005(n) for all the proper divisors d of n, otherwise 0. Here A344005(n) is the smallest positive integer m such that n divides m*(m+1).
2
1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1
OFFSET
1
FORMULA
a(n) = [A354991(n) = 1] = [A354999(n) = 1], where [ ] is the Iverson bracket.
MATHEMATICA
s[n_] := Module[{m = 1}, While[! Divisible[m*(m + 1), n], m++]; m]; a[n_] := Module[{sn = s[n]}, If[DivisorSum[n, If[s[#] < sn, 0, 1] &, # < n &] == 0, 1, 0]]; Array[a, 100] (* Amiram Eldar, Jun 17 2022 *)
PROG
(PARI)
A344005(n) = for(m=1, oo, if((m*(m+1))%n==0, return(m))); \\ From A344005
A354993(n) = { my(x=A344005(n)); fordiv(n, d, if(A344005(d)==x, return(d==n))); };
CROSSREFS
Characteristic function of A354994.
Cf. also A344880, A345950.
Sequence in context: A359590 A104521 A317198 * A131379 A359819 A284677
KEYWORD
nonn
AUTHOR
Antti Karttunen, Jun 17 2022
STATUS
approved