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 A216213 Numbers k such that sigma*(k) = Sum_{j=anti-divisors of k} sigma*(j), where sigma*(k) is the sum of the anti-divisors of k. 1
 1, 2, 11, 12, 15, 16, 22, 31, 76, 152, 309, 1576, 375479, 781314, 1114986, 3734218, 24311881, 68133239, 147881549 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Tested up to k = 108122. a(20) > 3*10^8. - Donovan Johnson, Mar 22 2013 LINKS Table of n, a(n) for n=1..19. EXAMPLE Anti-divisors of 76 are 3, 8, 9, 17 and 51 and their sum is 88. Anti-divisor of 3 is 2 -> Sum is 2. Anti-divisors of 8 are 3 and 5 -> Sum is 8. Anti-divisors of 9 are 2 and 6 -> Sum is 8. Anti-divisors of 17 are 2, 3, 5, 7 and 11 -> Sum is 28. Anti-divisors of 51 are 2, 6 and 34 -> Sum is 42. Finally, 2+8+8+28+42=88. MAPLE A216213:= proc(q) local a, b, c, j, k, n; for n from 1 to q do a:={}; b:=0; for k from 2 to n-1 do if abs((n mod k)-k/2)<1 then b:=b+k; a:=a union {k}; fi; od; c:=0; for j from 1 to nops(a) do for k from 2 to a[j]-1 do if abs((a[j] mod k)-k/2)<1 then c:=c+k; fi; od; od; if b=c then print(n); fi; od; end: A216213(10^10); CROSSREFS Cf. A066272, A178029, A191580, A191581, A192282-A192284. Sequence in context: A059192 A087339 A345922 * A160948 A299973 A136971 Adjacent sequences: A216210 A216211 A216212 * A216214 A216215 A216216 KEYWORD nonn AUTHOR Paolo P. Lava, Mar 13 2013 EXTENSIONS a(13)-a(19) from Donovan Johnson, Mar 22 2013 STATUS approved

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Last modified May 30 02:46 EDT 2024. Contains 372957 sequences. (Running on oeis4.)