cp's OEIS Frontend

A361201 Product of the right half (exclusive) of the multiset of prime factors of n; a(1) = 0.

%I A361201 #11 Aug 13 2024 09:10:30
%S A361201 0,1,1,2,1,3,1,2,3,5,1,3,1,7,5,4,1,3,1,5,7,11,1,6,5,13,3,7,1,5,1,4,11,
%T A361201 17,7,9,1,19,13,10,1,7,1,11,5,23,1,6,7,5,17,13,1,9,11,14,19,29,1,15,1,
%U A361201 31,7,8,13,11,1,17,23,7,1,9,1,37,5,19,11,13,1
%N A361201 Product of the right half (exclusive) of the multiset of prime factors of n; a(1) = 0.
%H A361201 Robert Israel, <a href="/A361201/b361201.txt">Table of n, a(n) for n = 1..10000</a>
%F A361201 A361200(n) * A347044(n) = n.
%F A361201 A361201(n) * A347043(n) = n.
%e A361201 The prime factors of 250 are {2,5,5,5}, with right half (exclusive) {5,5}, with product 25, so a(250) = 25.
%p A361201 f:= proc(n) local F;
%p A361201   F:= ifactors(n)[2];
%p A361201   F:= sort(map(t -> t[1]$t[2],F));
%p A361201   convert(F[ceil(nops(F)/2)+1 ..-1],`*`)
%p A361201 end proc:
%p A361201 f(1):= 0:
%p A361201 map(f, [$1..100]); # _Robert Israel_, Aug 12 2024
%t A361201 Table[If[n==1,0,Times@@Take[Join@@ConstantArray@@@FactorInteger[n],-Floor[PrimeOmega[n]/2]]],{n,100}]
%Y A361201 Positions of 1's are A000040.
%Y A361201 Positions of first appearances are A123666.
%Y A361201 The left inclusive version A347043.
%Y A361201 The inclusive version is A347044.
%Y A361201 The left version is A361200.
%Y A361201 A000005 counts divisors.
%Y A361201 A001221 counts distinct prime factors.
%Y A361201 A006530 gives greatest prime factor.
%Y A361201 A112798 lists prime indices, length A001222, sum A056239.
%Y A361201 A360616 gives half of bigomega (exclusive), inclusive A360617.
%Y A361201 A360673 counts multisets by right sum (exclusive), inclusive A360671.
%Y A361201 First for prime indices, second for partitions, third for prime factors:
%Y A361201 - A360676 gives left sum (exclusive), counted by A360672, product A361200.
%Y A361201 - A360677 gives right sum (exclusive), counted by A360675, product A361201.
%Y A361201 - A360678 gives left sum (inclusive), counted by A360675, product A347043.
%Y A361201 - A360679 gives right sum (inclusive), counted by A360672, product A347044.
%Y A361201 Cf. A001248, A026424, A096825, A347045, A347046, A360005.
%K A361201 nonn,look
%O A361201 1,4
%A A361201 _Gus Wiseman_, Mar 10 2023