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Least m>n such that the number of prime factors of m and n differ by 1.
3

%I #12 Feb 24 2024 10:35:50

%S 2,4,4,5,6,7,9,9,11,11,14,14,14,17,17,18,21,21,21,21,23,23,25,27,27,

%T 27,33,33,33,33,33,36,37,37,37,42,38,41,41,42,46,46,46,46,46,47,49,54,

%U 50,51,52,54,55,63,59,63,59,59,62,63,62,63,65

%N Least m>n such that the number of prime factors of m and n differ by 1.

%H David A. Corneth, <a href="/A071192/b071192.txt">Table of n, a(n) for n = 1..10000</a>

%F abs(A001222(a(n)) - A001222(n)) = 1.

%e a(11) = 14 as 11 has one prime factor (counted with multiplicity) and 14 has 2 prime factors (counted with multiplicity) 14 the smallest number m > 11 such that the number of prime factors of m and 11 differ by 1. - _David A. Corneth_, Feb 23 2024

%o (PARI)

%o a(n) = {

%o my(b = bigomega(n));

%o for(i = n + 1, oo,

%o if(abs(bigomega(i)-b) == 1,

%o return(i)

%o )

%o )

%o } \\ _David A. Corneth_, Feb 23 2024

%Y Cf. A071191, A071193.

%K nonn

%O 1,1

%A _Reinhard Zumkeller_, May 15 2002