%I #9 May 20 2021 04:59:43
%S 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,
%T 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,
%U 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
%N a(n) = 1 if n can be written as a product of factorials (A000142), 0 otherwise; Characteristic function of Jordan-Polya numbers (A001013).
%H Antti Karttunen, <a href="/A344438/b344438.txt">Table of n, a(n) for n = 1..65536</a>
%H <a href="/index/Ch#char_fns">Index entries for characteristic functions</a>
%F For all n, a(n) <= A322585(n).
%o (PARI)
%o search_up_to = 120;
%o A076934(n) = for(k=2, oo , if(n%k, return(n), n /= k));
%o A093411(n) = if(!n,n, if(n%2, n, A093411(A076934(n)))); \\ _Antti Karttunen_, May 19 2021
%o 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
%o v001013 = A001013list(search_up_to);
%o A344438(n) = if(v001013[#v001013]<n,-(1/0),!!vecsearch(v001013,n));
%Y Cf. A000142, A001013 (positions of ones), A093373 (of zeros), A322585.
%K nonn
%O 1
%A _Antti Karttunen_, May 19 2021