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A165346
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Numbers such that the sum of the distinct prime factors is a fourth power.
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1
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1, 39, 55, 66, 117, 132, 158, 198, 264, 275, 316, 351, 396, 507, 528, 594, 605, 632, 726, 792, 1053, 1056, 1095, 1188, 1255, 1264, 1375, 1452, 1491, 1506, 1521, 1584, 1782, 2112, 2130, 2178, 2211, 2376, 2528, 2904, 3012, 3025, 3111, 3159, 3168, 3285, 3363
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OFFSET
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1,2
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COMMENTS
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This is the 4th row of the infinite array A(k,n) = n-th positive integer such that the sum of the distinct prime factors is of the form j^k for integers j, k. The 2nd row is A164722 (hence the current sequence is a proper subset of A164722). The 3rd row is A164788. The smallest integers whose sum of distinct prime factors is 4^4 are {1255, 1506, 3012, ...}. The smallest integers whose sum of distinct prime factors is 5^4 are {9255, 21455, ...}. The smallest integers whose sum of distinct prime factors is 6^4 are {6455, 7746, ...}. The smallest integers whose sum of distinct prime factors is 7^4 are {4798, 9596, ...}.
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LINKS
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FORMULA
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{n such that A008472(n) = k^4 for k an integer}.
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EXAMPLE
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a(2) = 39, because 39 = 3*13, and 3+13 = 16 = 2^4.
a(7) = 158, because 158 = 2*79, and 2+79 = 81 = 3^4.
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MAPLE
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A008472 := proc(n) add( p, p = numtheory[factorset](n)) ; end: isA000583 := proc(n) iroot(n, 4, 'exct') ; exct ; end: A165346 := proc(n) if n = 1 then 1; else for a from procname(n-1)+1 do if isA000583(A008472(a)) then RETURN(a); fi; od: fi; end: seq(A165346(n), n=1..80) ; # R. J. Mathar, Sep 20 2009
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MATHEMATICA
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a165346[n_] := Select[Range@n, IntegerQ[Power[Plus @@ Transpose[FactorInteger[#]][[1]], 1/4]] &]; a165346[3400] (* Michael De Vlieger, Jan 06 2015 *)
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PROG
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(PARI) isok(n) = my(f=factor(n)); ispower(vecsum(f[, 1]), 4); \\ Michel Marcus, Jan 06 2015
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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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STATUS
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approved
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