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 A258135 Let s denote the sum of the abundant numbers in the aliquot parts of x. Sequence lists numbers x such that sigma(s) = usigma(x), where usigma(x) is the sum of the unitary divisors of x (A034448). 1
 760, 918, 924, 1540, 4648, 6204, 8260, 15210, 20070, 21450, 27450, 30114, 41052, 47344, 50464, 55952, 60040, 60534, 61088, 63080, 77024, 77994, 81320, 99084, 117572, 132210, 136068, 150750, 169480, 215325, 215740, 226422, 309160, 476196, 495444, 505720, 530292 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS Amiram Eldar, Table of n, a(n) for n = 1..1000 EXAMPLE Aliquot parts of 760 are 1, 2, 4, 5, 8, 10, 19, 20, 38, 40, 76, 95, 152, 190, 380. Abundant numbers are 20, 40 and 380. Then sigma(20+40+380) = sigma(440) = 1080 = usigma(760). Aliquot parts of 918 are 1, 2, 3, 6, 9, 17, 18, 27, 34, 51, 54, 102, 153, 306, 459. Abundant numbers are 18, 54, 102 and 306. Then sigma(18+54+102+306) = sigma(480) = 1512 = usigma(918). Aliquot parts of 924 are 1, 2, 3, 4, 6, 7, 11, 12, 14, 21, 22, 28, 33, 42, 44, 66, 77, 84, 132, 154, 231, 308, 462. Abundant numbers are 12, 42, 66, 84, 132, 308 and 462. Then sigma(12+42+66+84+132+308+462) = sigma(1106) = 1920 = usigma(924). MAPLE with(numtheory); P:=proc(q) local a, b, d, k, n; for n from 1 to q do a:=sort([op(divisors(n))]); b:=0; d:=0; for k from 1 to nops(a)-1 do if sigma(a[k])>2*a[k] then b:=b+a[k]; fi; od; for k from 1 to nops(a) do if gcd(a[k], n/a[k])=1 then d:=d+a[k]; fi; od; if sigma(b)=d then print(n); fi; od; end: P(10^9); CROSSREFS Cf. A000203, A005101, A034448, A258135. Sequence in context: A034414 A157983 A014747 * A247400 A234892 A233879 Adjacent sequences:  A258132 A258133 A258134 * A258136 A258137 A258138 KEYWORD nonn AUTHOR Paolo P. Lava, May 21 2015 STATUS approved

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Last modified July 28 09:54 EDT 2021. Contains 346326 sequences. (Running on oeis4.)