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).

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

Links

Antti Karttunen, Table of n, a(n) for n = 1..100000

Index entries for characteristic functions

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. A344005, A354991, A354999.

Cf. also A344880, A345950.

Sequence in context: A359590 A104521 A317198 * A131379 A359819 A284677

Adjacent sequences: A354990 A354991 A354992 * A354994 A354995 A354996

Keyword

nonn

Author

Antti Karttunen, Jun 17 2022

Status

approved