A240940 Least number k >= 0 such that n! - k is a perfect power.
0, 1, 2, 8, 20, 44, 127, 320, 476, 3584, 12311, 4604, 74879, 414119, 2071775, 5703551, 11551671, 45680444, 442548224, 1960632176, 2657058876, 24923993276, 130518272975, 1478154932316, 5446454455004, 38610655379975, 204033398880671, 538347188396016, 3809155729331900, 27460809907547975, 52607402757814775
Offset: 1
Keywords
Programs
-
PARI
a(n)=for(k=0,n!,s=n!-k;if(ispower(s)||s==1,return(k))) n=1;while(n<50,print1(a(n),", ");n++)
-
PARI
a(n)=for(k=1, n!, if(2^k>n!, kk=k; break)); if(kk==1, return(0)); L=List([]); for(i=2, kk, listinsert(L, n!-floor(n!^(1/i))^i, 1)); listsort(L); L[1] vector(40, n, a(n)) \\ faster program