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%I #20 Oct 18 2020 03:10:15
%S 2,3,4,5,6,7,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,25,26,28,29,
%T 30,31,33,34,35,36,37,38,39,41,42,43,44,45,46,47,48,49,50,51,52,53,55,
%U 57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,73,74,75,76,77,78,79,80,81,82,83
%N Let n = 2^e_2 * 3^e_3 * 5^e_5 * ... be the prime factorization of n; sequence gives n such that 1 + max{e_2, e_3, ...} is a prime.
%C The old entry with this sequence number was a duplicate of A004555.
%C Sequence is of positive density. - _Charles R Greathouse IV_, Dec 07 2012
%C The asymptotic density of this sequence is Sum_{p prime} (1/zeta(p) - 1/zeta(p-1)) = 0.8817562193... - _Amiram Eldar_, Oct 18 2020
%H Amiram Eldar, <a href="/A096432/b096432.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..881 from R. J. Mathar)
%p (Maple code for this entry and A074661)
%p M:=2000; ans1:=[]; ans2:=[];
%p for n from 1 to M do
%p t1:=op(2..-1, ifactors(n)); t2:=nops(t1);
%p m1:=0; for i from 1 to t2 do m1:=max(m1,t1[i][2]); od:
%p if isprime(1+m1) then ans1:=[op(ans1),n]; fi;
%p if isprime(m1) then ans2:=[op(ans2),n]; fi;
%p od:
%t Select[Range[2, 100], PrimeQ[1 + Max[FactorInteger[#][[;; , 2]]]] &] (* _Amiram Eldar_, Oct 18 2020 *)
%o (PARI) isA096432(n) = if(n<2,0,isprime(vecmax(factor(n)[,2])+1))
%Y Cf. A060476, A074661.
%K nonn
%O 1,1
%A _N. J. A. Sloane_, Sep 18 2008
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