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A376154 Numbers that are not the sum of the nonprime divisors of k for any k.

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%I A376154 #6 Sep 13 2024 08:07:19
%S A376154 0,2,3,4,6,8,9,12,14,17,18,19,20,21,24,25,28,30,31,32,33,38,41,42,43,
%T A376154 44,45,46,48,49,51,53,54,57,60,64,65,67,68,69,72,73,74,76,77,79,80,81,
%U A376154 82,85,89,90,91,93,97,98,99,100,101,102,103,104,105,106,108,109,110,113,114,117,121,126
%N A376154 Numbers that are not the sum of the nonprime divisors of k for any k.
%C A376154 Nonnegative numbers that do not appear in A023890.
%C A376154 If k > 1 and k = A023890(m), then m must be composite with m < k.  Thus k is a term of this sequence if k does not appear in A023890(1..k-1).
%H A376154 Robert Israel, <a href="/A376154/b376154.txt">Table of n, a(n) for n = 1..10000</a>
%e A376154 a(6) = 8 is a term because 8 is not A023890(1) = 1 or A023890(4) = 5 or A023890(6) = 7.
%p A376154 N:= 100: # to get terms <= N
%p A376154 f:= proc(n) convert(remove(isprime, numtheory:-divisors(n)),`+`) end proc:
%p A376154 S:= {$0..N} minus map(f, {$1..N-1}):
%p A376154 sort(convert(S,list));
%Y A376154 Cf. A023890.
%K A376154 nonn
%O A376154 1,2
%A A376154 _Robert Israel_, Sep 12 2024