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Prime numbers that cannot be written as the sum of a prime number and a superior highly composite number.
0

%I #16 Sep 30 2024 12:36:12

%S 2,3,307,911,1201,1259,1693,2179,2381,2927,3191,3499,3557,4201,4441,

%T 4721,5573,6121,7207,8219,8273,8537,8627,8999,9137,9203,9811,10133,

%U 10357,11597,12211,12343,13217,13421,13921,15053,15401,15551,15959,15991,16411,16561,17117,17207

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

%e 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 (Python)

%o from sympy import *

%o SHCN = [2, 6, 12, 60, 120, 360, 2520, 5040, 55440, 720720]

%o for x in range(3, 16000, 2):

%o waysFound = 0

%o if isprime(x):

%o iterC = 0

%o while iterC < len(SHCN) and SHCN[iterC] < x:

%o if isprime(x - SHCN[iterC]):

%o waysFound += 1

%o iterC += 1

%o if waysFound == 0:

%o print(x)

%Y Cf. A000040, A002201, A375866.

%K nonn

%O 1,1

%A _Walter Robinson_, Aug 31 2024