A345950 a(n) = 1 if for all proper divisors d of n, A002034(d) < A002034(n), otherwise 0.

1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0

Offset

1

Links

Antti Karttunen, Table of n, a(n) for n = 1..65537

Index entries for characteristic functions

Index entries for sequences related to factorial numbers

Formula

a(n) = A010055(n) - [n is in A345946], where [ ] is the Iverson bracket.

For all n >= 1, A010051(n) <= a(n) <= A010055(n).

Prog

(PARI)
A002034(n) = if(1==n, n, my(s=factor(n)[, 1], k=s[#s], f=Mod(k!, n)); while(f, f*=k++); (k)); \\ After code in A002034.
A345950(n) = { my(x=A002034(n)); fordiv(n, d, if(A002034(d)==x, return(d==n))); };

Crossrefs

Characteristic function of A345944.

Cf. A002034, A010051, A010055, A345945 (positions of zeros), A345946.

Cf. also A344880.

Sequence in context: A071034 A089497 A355937 * A122895 A333248 A114592

Adjacent sequences: A345947 A345948 A345949 * A345951 A345952 A345953

Keyword

nonn

Author

Antti Karttunen, Jul 04 2021

Status

approved