A302785 - OEIS

%I #7 Apr 16 2018 22:10:36

%S 0,1,2,3,4,2,5,3,6,4,7,3,8,5,4,9,10,6,11,4,5,7,12,3,13,8,6,5,14,4,15,

%T 9,7,10,5,6,16,11,8,4,17,5,18,7,6,12,19,9,20,13,10,8,21,6,7,5,11,14,

%U 22,4,23,15,6,9,8,7,24,10,12,5,25,6,26,16,13,11,7,8,27,9,28,17,29,5,10,18,14,7,30,6,8,12,15,19,11,9,31,20,7,13,32,10,33,8,5

%N Index of the largest Fermi-Dirac factor of n, a(1) = 0 by convention: a(n) = A302778(A223491(n)).

%H Antti Karttunen, <a href="/A302785/b302785.txt">Table of n, a(n) for n = 1..65537</a>

%F a(n) = A302778(A223491(n)).

%F For n > 1, A050376(a(n)) = A223491(n).

%F For n >= 1, a(A050376(n)) = n.

%o (PARI)

%o up_to = 65537;

%o v050376 = vector(up_to);

%o A050376(n) = v050376[n];

%o ispow2(n) = (n && !bitand(n,n-1));

%o i = 0; for(n=1,oo,if(ispow2(isprimepower(n)), i++; v050376[i] = n); if(i == up_to,break));

%o A302785(n) = if(1==n,0, my(e); fordiv(n, d, if(ispow2(isprimepower(n/d)), e = vecsearch(v050376, n/d); if(e, return(e), print("v050376 too short!"); return(1/0)))));

%Y A left inverse of A050376.

%Y Cf. A052331, A223491, A240535, A302778, A302786, A302788, A302789 (ordinal transform).

%Y Cf. also A061395.

%K nonn

%O 1,3

%A _Antti Karttunen_, Apr 13 2018