A344438 a(n) = 1 if n can be written as a product of factorials (A000142), 0 otherwise; Characteristic function of Jordan-Polya numbers (A001013).

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

Offset

1

Links

Antti Karttunen, Table of n, a(n) for n = 1..65536

Index entries for characteristic functions

Formula

For all n, a(n) <= A322585(n).

Prog

(PARI)
search_up_to = 120;
A076934(n) = for(k=2, oo , if(n%k, return(n), n /= k));
A093411(n) = if(!n, n, if(n%2, n, A093411(A076934(n)))); \\ Antti Karttunen, May 19 2021
A001013list(lim, mx=lim)=if(lim<2, return([1])); my(v=[1], t=1); for(n=2, mx, t*=n; if(t>lim, break); v=concat(v, t*A001013list(lim\t, t))); Set(v) \\ From A001013
v001013 = A001013list(search_up_to);
A344438(n) = if(v001013[#v001013]<n, -(1/0), !!vecsearch(v001013, n));

Crossrefs

Cf. A000142, A001013 (positions of ones), A093373 (of zeros), A322585.

Sequence in context: A380417 A141735 A343999 * A322585 A326956 A341629

Adjacent sequences: A344435 A344436 A344437 * A344439 A344440 A344441

Keyword

nonn

Author

Antti Karttunen, May 19 2021

Status

approved