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Numbers having more prime factors than their neighbors together.
2

%I #10 Dec 16 2021 10:38:57

%S 12,16,18,24,30,32,36,40,42,48,54,60,64,72,84,88,90,96,102,108,112,

%T 120,128,132,138,140,144,150,156,160,162,168,180,192,198,200,210,216,

%U 224,228,234,240,250,252,256,264,270,272,280,282,288,294,300,304,306,308

%N Numbers having more prime factors than their neighbors together.

%H Michael S. Branicky, <a href="/A097620/b097620.txt">Table of n, a(n) for n = 1..10000</a>

%F {k: A001222(k) > A001222(k-1) + A001222(k+1)}. - _Michael S. Branicky_, Dec 16 2021

%e A001222(64) = A001222(2^6) = 6, A001222(64-1) = A001222(3*3*7) = 3, A001222(64+1) = A001222(5*13) = 2, and 6 > 3+2, therefore 64 is a term.

%o (Python)

%o from sympy import primeomega

%o def ok(n): return primeomega(n) > primeomega(n-1) + primeomega(n+1)

%o print([k for k in range(2, 309) if ok(k)]) # _Michael S. Branicky_, Dec 16 2021

%Y Subsequence of A097619.

%Y Cf. A001222.

%K nonn

%O 1,1

%A _Reinhard Zumkeller_, Aug 17 2004