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A194196
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Numbers k such that the sum of the divisors of k and the sum of the distinct prime divisors of k are both a square.
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1
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1, 66, 94, 1092, 1146, 1416, 1491, 1782, 2130, 2159, 2805, 3012, 3531, 4836, 8736, 9065, 9911, 12532, 13156, 15960, 16194, 24096, 25866, 27652, 29316, 29484, 30942, 34162, 34782, 34860, 37736, 37884, 38232, 38688, 40257, 41331, 48204, 51460, 54162, 54411
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OFFSET
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1,2
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LINKS
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FORMULA
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EXAMPLE
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94 is in the sequence because the distinct prime divisors are {2,47} -> sum = 7^2, and the divisors are {1,2,47,94} -> sum = 12^2.
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MAPLE
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isA006532 :=proc(n) issqr(numtheory[sigma](n)) ; end proc:
A008472 := proc(n) add(d, d=numtheory[factorset](n)) ; end proc:
isA164722 :=proc(n) issqr(A008472(n)) ; end proc:
for n from 1 to 50000 do if isA006532(n) and isA164722(n) then printf("%d, ", n); end if; end do; # R. J. Mathar, Aug 18 2011
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PROG
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(PARI) isok(k) = my(f=factor(k)); issquare(sigma(f)) && issquare(vecsum(f[, 1])); \\ Michel Marcus, Dec 05 2020
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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