A302788 Number of times the smallest Fermi-Dirac factor of n is the smallest Fermi-Dirac factor for numbers <= n; a(1) = 1.

1, 1, 1, 1, 1, 2, 1, 3, 1, 4, 1, 2, 1, 5, 3, 1, 1, 6, 1, 2, 4, 7, 1, 8, 1, 9, 5, 3, 1, 10, 1, 11, 6, 12, 2, 4, 1, 13, 7, 14, 1, 15, 1, 5, 3, 16, 1, 8, 1, 17, 9, 6, 1, 18, 4, 19, 10, 20, 1, 11, 1, 21, 2, 7, 5, 22, 1, 8, 12, 23, 1, 24, 1, 25, 13, 9, 3, 26, 1, 6, 1, 27, 1, 14, 7, 28, 15, 29, 1, 30, 4, 10, 16, 31, 8, 32, 1, 33, 2, 11, 1, 34, 1, 35, 17

Offset: 1

Author

Antti Karttunen, Apr 13 2018

Keywords

• nonn

Comments

Ordinal transform of A223490, or equally, of A302786.

Links

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

Crossrefs

Cf. A001511, A050376, A052331, A223490, A302786, A302789.

Cf. A084400 (gives the positions of 1's).

Cf. also A078898.

Programs

PARI

up_to = 65537;
ordinal_transform(invec) = { my(om = Map(), outvec = vector(length(invec)), pt); for(i=1, length(invec), if(mapisdefined(om,invec[i]), pt = mapget(om, invec[i]), pt = 0); outvec[i] = (1+pt); mapput(om,invec[i],(1+pt))); outvec; };
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));
A052331(n) = { my(s=0,e); while(n > 1, fordiv(n, d, if(((n/d)>1)&&ispow2(isprimepower(n/d)), e = vecsearch(v050376, n/d); if(!e, print("v050376 too short!"); return(1/0)); s += 2^(e-1); n = d; break))); (s); };
A001511(n) = 1+valuation(n,2);
A302786(n) = if(1==n, 0, A001511(A052331(n)));
v302788 = ordinal_transform(vector(up_to,n,A302786(n)));
A302788(n) = v302788[n];