A389079 Odd nonsquarefree numbers k such that {sum of unitary divisors of k} plus {sum of squarefree divisors of k} >= 2*k.

315, 495, 585, 3465, 4095, 5355, 5775, 5985, 6435, 6825, 7245, 8085, 8415, 8925, 9009, 9135, 9405, 9555, 9765, 9945, 9975, 10725, 11115, 11385, 11655, 11781, 12075, 12495, 12705, 12915, 13167, 13455, 13545, 13923, 14355, 14535, 14805, 15225, 15345, 15561, 15939, 16275, 16695, 16965, 17595, 18135, 18315, 18585, 19215

Offset

1,1

Comments

Odd terms k of A013929 for which A325973(k) >= k, or equally, A325977(k) >= 0.

It is conjectured that there are no common terms with A228058 (see also A388986), and for all terms, A001221(a(n)) >= 3.

Links

Antti Karttunen, Table of n, a(n) for n = 1..10000

Formula

{k | k == 1 (mod 2), A008683(k) = 0 and A034448(k)+A048250(k) >= 2*k}.

Prog

(PARI)
A325973(n) = (1/2)*sumdiv(n, d, d*(issquarefree(d) + (1==gcd(d, n/d))));
is_A389079(k) = ((k%2) && !issquarefree(k) && (A325973(k) >= k));

Crossrefs

Intersection of A053850 and A389215.

Cf. A001221, A034448, A048250, A228058, A325973, A325977, A388986.

Sequence in context: A256575 A295990 A349868 * A349937 A076773 A114807

Adjacent sequences: A389076 A389077 A389078 * A389080 A389081 A389082

Keyword

nonn

Author

Antti Karttunen, Sep 30 2025

Status

approved