A302785 Index of the largest Fermi-Dirac factor of n, a(1) = 0 by convention: a(n) = A302778(A223491(n)).

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, 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, 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

Offset: 1

Author

Antti Karttunen, Apr 13 2018

Keywords

• nonn

Links

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

Crossrefs

A left inverse of A050376.

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

Cf. also A061395.

Programs

PARI

up_to = 65537;
v050376 = vector(up_to);
A050376(n) = v050376[n];
ispow2(n) = (n && !bitand(n,n-1));
i = 0; for(n=1,oo,if(ispow2(isprimepower(n)), i++; v050376[i] = n); if(i == up_to,break));
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)))));

Formula

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

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

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