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A086486
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Numbers n such that the sum of the distinct prime divisors divides rad(n)=A007947(n).
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7
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2, 3, 4, 5, 7, 8, 9, 11, 13, 16, 17, 19, 23, 25, 27, 29, 30, 31, 32, 37, 41, 43, 47, 49, 53, 59, 60, 61, 64, 67, 70, 71, 73, 79, 81, 83, 89, 90, 97, 101, 103, 105, 107, 109, 113, 120, 121, 125, 127, 128, 131, 137, 139, 140, 149, 150, 151, 157, 163, 167
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OFFSET
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1,1
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COMMENTS
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Every prime power is a member.
Numbers with exactly two distinct prime divisors are not members of the sequence. - Victoria A Sapko (vsapko(AT)canes.gsw.edu), Sep 23 2003
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LINKS
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EXAMPLE
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30 is a member. The prime divisors of 30 are 2,3 and 5 and 2+3+5 = 10, divides 30.
84, however, is not a member because the sum of its distinct prime divisors (2+3+7=12) does not divide the product of its distinct prime divisors (2*3*7=42), even though 12 does divide 84. [From Harvey P. Dale, Nov 26 2011, based on a comment from Ray Chandler]
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MATHEMATICA
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sdpQ[n_]:=Module[{dpds=Transpose[FactorInteger[n]][[1]]}, Divisible[ Times@@dpds, Total[dpds]]]; Select[Range[2, 200], sdpQ] (* Harvey P. Dale, Nov 26 2011 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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More terms from Victoria A Sapko (vsapko(AT)canes.gsw.edu), Sep 23 2003
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STATUS
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approved
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