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A375864 Prime numbers that cannot be written as the sum of a prime number and a superior highly composite number.

%I A375864 #16 Sep 30 2024 12:36:12
%S A375864 2,3,307,911,1201,1259,1693,2179,2381,2927,3191,3499,3557,4201,4441,
%T A375864 4721,5573,6121,7207,8219,8273,8537,8627,8999,9137,9203,9811,10133,
%U A375864 10357,11597,12211,12343,13217,13421,13921,15053,15401,15551,15959,15991,16411,16561,17117,17207
%N A375864 Prime numbers that cannot be written as the sum of a prime number and a superior highly composite number.
%e A375864 The prime number 37 can be written as the sum of prime number 31 and superior highly composite number 6 and thus is not in this sequence.
%o A375864 (Python)
%o A375864 from sympy import *
%o A375864 SHCN = [2, 6, 12, 60, 120, 360, 2520, 5040, 55440, 720720]
%o A375864 for x in range(3, 16000, 2):
%o A375864     waysFound = 0
%o A375864     if isprime(x):
%o A375864         iterC = 0
%o A375864         while iterC < len(SHCN) and SHCN[iterC] < x:
%o A375864             if isprime(x - SHCN[iterC]):
%o A375864                 waysFound += 1
%o A375864             iterC += 1
%o A375864         if waysFound == 0:
%o A375864             print(x)
%Y A375864 Cf. A000040, A002201, A375866.
%K A375864 nonn
%O A375864 1,1
%A A375864 _Walter Robinson_, Aug 31 2024