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A357462 Numbers whose sum of deficient divisors is equal to their sum of nondeficient divisors. 3
6, 28, 30, 42, 66, 78, 102, 114, 138, 150, 174, 186, 222, 246, 258, 282, 294, 308, 318, 330, 354, 364, 366, 390, 402, 426, 438, 462, 474, 476, 496, 498, 510, 532, 534, 546, 570, 582, 606, 618, 642, 644, 654, 678, 690, 714, 726, 750, 762, 786, 798, 812, 822, 834 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Numbers k such that A187793(k) = A187794(k) + A187795(k).
All the terms are nondeficient numbers (A023196).
All the perfect numbers (A000396) are terms.
This sequence is infinite: if k = 2^(p-1)*(2^p-1) is an even perfect number and q > 2^p-1 is a prime, then k*q is a term.
Since the total sum of divisors of any term is even, none of the terms are squares or twice squares.
Are there odd terms in this sequence? There are none below 10^10.
The numbers of terms not exceeding 10^k, for k = 1, 2, ..., are 1, 6, 63, 605, 6164, 61291, 614045, 6139193, 61382607, 613861703, ... . Apparently, the asymptotic density of this sequence exists and equals 0.06138... .
LINKS
EXAMPLE
6 is a term since the sum of its deficient divisors, 1 + 2 + 3 is equal to 6, its only nondeficient divisor.
30 is a term since the sum of its deficient divisors, 1 + 2 + 3 + 5 + 10 + 15 = 36 is equal to the sum of its nondeficient divisors, 6 + 30 = 36.
MATHEMATICA
q[n_] := DivisorSum[n, If[DivisorSigma[-1, #] < 2, #, -#] &] == 0; Select[Range[1000], q]
PROG
(PARI) is(n) = sumdiv(n, d, if(sigma(d, -1) < 2, d, -d)) == 0;
CROSSREFS
Subsequence of A023196 and A028983.
A000396 is a subsequence.
Sequence in context: A211679 A261868 A342922 * A105402 A362805 A145551
KEYWORD
nonn
AUTHOR
Amiram Eldar, Sep 29 2022
STATUS
approved

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Last modified June 22 08:18 EDT 2024. Contains 373567 sequences. (Running on oeis4.)