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%I #39 Oct 04 2021 08:11:19
%S 30,66,70,102,105,138,165,170,174,231,255,258,273,282,318,322,345,354,
%T 374,399,406,426,435,455,470,483,498,506,530,561,595,602,606,618,627,
%U 642,682,705,715,759,786,795,805,822,830,885,894,903,957,978,987,1001
%N Numbers k the smallest solution of A023900(m) = s, m >= 1, s <> 0, such that A023900(k) is negative and k is nonprime.
%C The least solutions of A023900(m) = -s contains the sequence A000040. The union of this sequence and A000040 make up all of the least solutions of A023900(n) = -s.
%C Terms of this sequence are the product of an odd number of prime factors.
%C A000010(a(n)) is nonsquarefree, for n >= 1.
%C Every a(n) is one part of a pair (a(n), x) where A023900(x) = -A023900(a(n)) and x is the least solution of A023900(m) = s, and A023900(x) is positive. Where this is the case A000010(x) = A000010(a(n)).
%F A000010(a(n)) + A023900(a(n)) = 0.
%F tau(a(n)) mod 8 = 0.
%e 30 is a term as it is the least solution to A023900(m) = -8 and is nonprime.
%e 66 is a term as it is the least solution to A023900(m) = -20 and is nonprime.
%e 4 is not a term since A023900(4) = -1, and the smallest solution of A023909(m) = -1 is 2 and is prime.
%o (PARI) f(n) = sumdivmult(n, d, d*moebius(d)); \\ from A023900
%o lista(nn) = {va = []; for (n=2, nn, x = f(n); if ((x = f(n)) < 0, if (! isprime(n) && !vecsearch(va, x), print1(n, ", ")); va = vecsort(concat(va, x),,8);););} \\ _Michel Marcus_, Mar 14 2018
%Y Cf. A023900, A000010, A008683, A000010.
%K nonn
%O 1,1
%A _Torlach Rush_, Mar 12 2018
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