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 A192279 Anti-hypersigma(n): sum of the anti-divisors of n plus the recursive sum of the anti-divisors of the anti-divisors until 2 is reached. 1
 2, 5, 7, 9, 19, 17, 17, 40, 33, 37, 45, 40, 67, 49, 89, 96, 65, 88, 71, 134, 127, 91, 189, 120, 187, 170, 91, 166, 151, 219, 243, 164, 261, 140, 315, 392, 233, 310, 247, 374, 245, 150, 461, 280, 285, 347, 407, 468, 215, 538, 515, 234, 565, 422, 609, 532, 495 (list; graph; refs; listen; history; text; internal format)
 OFFSET 3,1 COMMENTS Similar to A191150 but using anti-divisors. The recursion is stopped when 2 is reached because 2 has no anti-divisors. LINKS Paolo P. Lava, Table of n, a(n) for n = 3..5000 EXAMPLE n=14 -> anti-divisors are 3,4,9. We start with 3+4+9=16. Now for 3, 4 and 9 we repeat the procedure: 3-> 2 -> no anti-divisors. To add: 2. 4-> 3 -> 2 -> no anti-divisors. To add: 3+2=5. 9-> 2,6. To add: 2+6=8. --- 2 -> no anti-divisors. --- 6 -> 4 -> 3 -> 2 -> no anti-divisors. To add: 4+3+2=9. Total is 16+2+5+8+9=40. MAPLE with(numtheory); P:=proc(n) local a, b, c, k, s; a:={}; for k from 2 to n-1 do if abs((n mod k)- k/2) < 1 then a:=a union {k}; fi; od; b:=nops(a); c:=op(a); s:=0; if b>1 then   for k from 1 to b do s:=s+c[k]; od; else s:=c; fi; b:=nops(a); c:=(sort([op(a)])); for k from 1 to b do if c[k]>2 then s:=s+P(c[k]); fi; od; s; end: Antihps:=proc(i) local n; for n from 1 to i do print(P(n)); od; end: CROSSREFS Cf. A066272, A191150. Sequence in context: A211167 A083272 A115906 * A286356 A086422 A046880 Adjacent sequences:  A192276 A192277 A192278 * A192280 A192281 A192282 KEYWORD nonn,easy AUTHOR Paolo P. Lava, Jul 13 2011 STATUS approved

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Last modified March 18 16:00 EDT 2019. Contains 321292 sequences. (Running on oeis4.)