A332979 Largest integer m satisfying Omega(m) + pi(gpf(m)) - [m<>1] = n.

1, 2, 4, 9, 27, 125, 625, 3125, 16807, 161051, 1771561, 19487171, 214358881, 2357947691, 25937424601, 285311670611, 3138428376721, 34522712143931, 582622237229761, 9904578032905937, 168377826559400929, 2862423051509815793, 48661191875666868481

Offset

0,2

Comments

From Michael De Vlieger, Aug 22 2022: (Start)

Subset of A000961.

Maxima of row n of A005940.

Maxima of row n of A182944 and row n of A182945. (End)

Links

Alois P. Heinz, Table of n, a(n) for n = 0..461

Michael De Vlieger, Concise table of n, a(n) for n = 1..10000, where a(n) = prime(k)^e written as "pk^e". (a(0) = 1 is presented as "p1^0" to avoid reconversion errors in some CAS associated with "prime(0)".)

Michael De Vlieger, Annotated plot of a(n) = prime(k)^e at (x,y) = (e,k) for n = 1..64, showing the first and last terms divisible by prime(k) in red, singleton powers of prime(k) in green, otherwise blue.

Michael De Vlieger, Plot of a(n) = prime(k)^e at (x,y) = (e,k) for n = 1..10000.

Michael De Vlieger, Fan style binary tree showing row m = 2..15 of A005940 in concentric semicircles. Terms in light blue appear in row m-1 of A182944, highlighting a(m-1) in red.

Michael De Vlieger, Fan style binary tree showing row m = 2..15 of A005940 in concentric semicircles. We apply a color function with dark blue the minimum and greens the largest values to show the magnitude of terms in row m compared to 2^(m-1). The row maximum a(m-1) appears in red.

Wikipedia, Iverson bracket

Formula

a(n) = A332977(A011782(n)).

Maple

b:= proc(n, i) option remember; `if`(n=0, 1, max(seq(b(n-
     `if`(i=0, j, 1), j)*ithprime(j), j=1..`if`(i=0, n, i))))
    end:
a:= n-> b(n, 0):
seq(a(n), n=0..23);

Mathematica

b[n_, i_] := b[n, i] = If[n == 0, 1, Max[Table[
     b[n - If[i == 0, j, 1], j] Prime[j], {j, 1, If[i == 0, n, i]}]]];
a[n_] := b[n, 0];
a /@ Range[0, 23] (* Jean-François Alcover, May 03 2021, after Alois P. Heinz *)
(* Second program: extract data from the concise a-file of 10000 terms: *)
With[{nn = 23 (* set nn <= 10000 as desired *)}, Prime[#1]^#2 & @@ # & /@ Map[ToExpression /@ {StringTrim[#1, "p"], #2} & @@ StringSplit[#, "^"] &, Import["https://oeis.org/A332979/a332979.txt", "Data"][[1 ;; nn, -1]] ] ] (* Michael De Vlieger, Aug 22 2022 *)

Crossrefs

Cf. A000720 (pi), A001222 (Omega), A006530 (GPF), A011782, A060576 ([n<>1]), A061395 (pi(gpf(n))), A332977.

Sequence in context: A007876 A343845 A349404 * A176068 A296264 A343166

Adjacent sequences: A332976 A332977 A332978 * A332980 A332981 A332982

Keyword

nonn

Author

Alois P. Heinz, Mar 04 2020

Status

approved