A300790 Numbers k the smallest solution of A023900(m) = s, m >= 1, s <> 0, such that A023900(k) is negative and k is nonprime.

30, 66, 70, 102, 105, 138, 165, 170, 174, 231, 255, 258, 273, 282, 318, 322, 345, 354, 374, 399, 406, 426, 435, 455, 470, 483, 498, 506, 530, 561, 595, 602, 606, 618, 627, 642, 682, 705, 715, 759, 786, 795, 805, 822, 830, 885, 894, 903, 957, 978, 987, 1001

Offset

1,1

Comments

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.

Terms of this sequence are the product of an odd number of prime factors.

A000010(a(n)) is nonsquarefree, for n >= 1.

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)).

Links

Table of n, a(n) for n=1..52.

Formula

A000010(a(n)) + A023900(a(n)) = 0.

tau(a(n)) mod 8 = 0.

Example

30 is a term as it is the least solution to A023900(m) = -8 and is nonprime.
66 is a term as it is the least solution to A023900(m) = -20 and is nonprime.
4 is not a term since A023900(4) = -1, and the smallest solution of A023909(m) = -1 is 2 and is prime.

Prog

(PARI) f(n) = sumdivmult(n, d, d*moebius(d)); \\ from A023900
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

Crossrefs

Cf. A023900, A000010, A008683, A000010.

Sequence in context: A320705 A132771 A326158 * A175259 A044132 A044513

Adjacent sequences: A300787 A300788 A300789 * A300791 A300792 A300793

Keyword

nonn

Author

Torlach Rush, Mar 12 2018

Status

approved