

A099637


Numbers such that gcd(Sum,n) = A099635 and gcd(Sum,Product) = A099636 are not identical. Sum and Product here are the sum and product of all distinct prime factors of n.


0



84, 132, 168, 228, 234, 252, 260, 264, 276, 308, 336, 340, 372, 396, 456, 468, 504, 516, 520, 528, 532, 552, 558, 564, 580, 588, 616, 644, 672, 680, 684, 702, 708, 740, 744, 756, 792, 804, 820, 828, 836, 852, 855, 868, 884, 912, 936, 948, 996, 1008, 1012, 1032
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OFFSET

1,1


COMMENTS

Of the first million integers, 75811 (of which 6300 are odd) belong to this sequence.  Robert G. Wilson v, Nov 04 2004


LINKS



EXAMPLE

84 is here because its factor list = {2,3,7} and sum = 2 + 3 + 7 = 12, product = 2*3*7 = 42, gcd(12,84) = 12, gcd(12,42) = 6 != 12.


MATHEMATICA

<<NumberTheory`NumberTheoryFunctions` pf[x_] :=PrimeFactorList[x]; a=Table[Max[pf[w]], {w, 2, m}]; Table[GCD[Apply[Plus, pf[w]], Apply[Plus, pf[w]]], {w, 1, 100}]
PrimeFactors[n_Integer] := Flatten[ Table[ # [[1]], {1}] & /@ FactorInteger[n]]; fQ[n_] := Block[{pf = PrimeFactors[n]}, GCD[Plus @@ pf, n] == GCD[Plus @@ pf, Times @@ pf]]; Select[ Range[1039], ! fQ[ # ] &] (* Robert G. Wilson v, Nov 04 2004 *)


CROSSREFS



KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



