A302789 - OEIS

A302789

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

1, 1, 1, 1, 1, 2, 1, 2, 1, 2, 1, 3, 1, 2, 3, 1, 1, 2, 1, 4, 3, 2, 1, 4, 1, 2, 3, 4, 1, 5, 1, 2, 3, 2, 5, 4, 1, 2, 3, 6, 1, 6, 1, 4, 5, 2, 1, 3, 1, 2, 3, 4, 1, 6, 5, 7, 3, 2, 1, 7, 1, 2, 7, 4, 5, 6, 1, 4, 3, 8, 1, 8, 1, 2, 3, 4, 7, 6, 1, 5, 1, 2, 1, 9, 5, 2, 3, 8, 1, 9, 7, 4, 3, 2, 5, 6, 1, 2, 9, 4, 1, 6, 1, 8, 10

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OFFSET

1,6

COMMENTS

Ordinal transform of A223491, or equally, of A302785.

LINKS

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

MATHEMATICA

f[n_] := Max@Table[{p, e} = pe; p^(2^(Length[IntegerDigits[e, 2]]-1)), {pe, FactorInteger[n]}];

b[_] = 1;

a[n_] := a[n] = With[{t = f[n]}, b[t]++];

Array[a, 105] (* Jean-François Alcover, Dec 18 2021 *)

PROG

(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; };

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

A223491(n) = if(1==n, n, fordiv(n, d, if(ispow2(isprimepower(n/d)), return(n/d))));

v302789 = ordinal_transform(vector(up_to, n, A223491(n)));

A302789(n) = v302789[n];

CROSSREFS

Cf. A050376, A052331, A223491, A302785, A302788.

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

Cf. also A078899.

Sequence in context: A337176 A033103 A245661 * A346089 A302776 A366510

Adjacent sequences: A302786 A302787 A302788 * A302790 A302791 A302792

KEYWORD

nonn

AUTHOR

Antti Karttunen, Apr 13 2018

STATUS

approved