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A357460
Numbers whose number of deficient divisors is equal to their number of nondeficient divisors.
3
72, 108, 120, 168, 180, 252, 420, 528, 560, 624, 1188, 1224, 1368, 1400, 1404, 1632, 1656, 1824, 1836, 1960, 1980, 2040, 2052, 2088, 2208, 2232, 2280, 2340, 2484, 2664, 2760, 2772, 2784, 2856, 2952, 2976, 3060, 3096, 3132, 3192, 3200, 3276, 3348, 3384, 3420, 3432
OFFSET
1,1
COMMENTS
Numbers k such that A080226(k) = A341620(k).
This sequence is infinite: if p >= 17 is a prime then 72*p is a term.
The least odd term of this sequence is a(36126824) = A357461(1) = 3010132125.
Since the number of divisors of any term is even, none of the terms are squares.
The numbers of terms not exceeding 10^k, for k = 2, 3, ..., are 1, 10, 131, 1172, 12003, 120647, 1199147, 11992293, 120089446, ... . Apparently, the asymptotic density of this sequence exists and is equal to about 0.012.
LINKS
EXAMPLE
72 is a term since it has 12 divisors, 6 of them (1, 2, 3, 4, 8 and 9) are deficient and 6 (6, 12, 18, 24, 36 and 72) are not.
MATHEMATICA
q[n_] := DivisorSum[n, If[DivisorSigma[-1, #] < 2, 1, -1] &] == 0; Select[Range[3500], q]
PROG
(PARI) is(n) = sumdiv(n, d, if(sigma(d, -1) < 2, 1, -1)) == 0;
CROSSREFS
Subsequence of A000037 and A005101.
Sequence in context: A205189 A258695 A102562 * A216426 A308053 A372404
KEYWORD
nonn
AUTHOR
Amiram Eldar, Sep 29 2022
STATUS
approved