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

%I A332979 #27 Aug 29 2022 20:26:38
%S A332979 1,2,4,9,27,125,625,3125,16807,161051,1771561,19487171,214358881,
%T A332979 2357947691,25937424601,285311670611,3138428376721,34522712143931,
%U A332979 582622237229761,9904578032905937,168377826559400929,2862423051509815793,48661191875666868481
%N A332979 Largest integer m satisfying Omega(m) + pi(gpf(m)) - [m<>1] = n.
%C A332979 From _Michael De Vlieger_, Aug 22 2022: (Start)
%C A332979 Subset of A000961.
%C A332979 Maxima of row n of A005940.
%C A332979 Maxima of row n of A182944 and row n of A182945. (End)
%H A332979 Alois P. Heinz, <a href="/A332979/b332979.txt">Table of n, a(n) for n = 0..461</a>
%H A332979 Michael De Vlieger, <a href="/A332979/a332979.txt">Concise table of n, a(n)</a> 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)".)
%H A332979 Michael De Vlieger, <a href="/A332979/a332979.png">Annotated plot of a(n) = prime(k)^e at (x,y) = (e,k)</a> 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.
%H A332979 Michael De Vlieger, <a href="/A332979/a332979_1.png">Plot of a(n) = prime(k)^e at (x,y) = (e,k)</a> for n = 1..10000.
%H A332979 Michael De Vlieger, <a href="/A332979/a332979_2.png">Fan style binary tree</a> 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.
%H A332979 Michael De Vlieger, <a href="/A332979/a332979_3.png">Fan style binary tree</a> 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.
%H A332979 Wikipedia, <a href="https://en.wikipedia.org/wiki/Iverson_bracket">Iverson bracket</a>
%F A332979 a(n) = A332977(A011782(n)).
%p A332979 b:= proc(n, i) option remember; `if`(n=0, 1, max(seq(b(n-
%p A332979      `if`(i=0, j, 1), j)*ithprime(j), j=1..`if`(i=0, n, i))))
%p A332979     end:
%p A332979 a:= n-> b(n, 0):
%p A332979 seq(a(n), n=0..23);
%t A332979 b[n_, i_] := b[n, i] = If[n == 0, 1, Max[Table[
%t A332979      b[n - If[i == 0, j, 1], j] Prime[j], {j, 1, If[i == 0, n, i]}]]];
%t A332979 a[n_] := b[n, 0];
%t A332979 a /@ Range[0, 23] (* _Jean-François Alcover_, May 03 2021, after _Alois P. Heinz_ *)
%t A332979 (* Second program: extract data from the concise a-file of 10000 terms: *)
%t A332979 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 *)
%Y A332979 Cf. A000720 (pi), A001222 (Omega), A006530 (GPF), A011782, A060576 ([n<>1]), A061395 (pi(gpf(n))), A332977.
%K A332979 nonn
%O A332979 0,2
%A A332979 _Alois P. Heinz_, Mar 04 2020