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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 (list; graph; refs; listen; history; text; internal format)
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

Table of n, a(n) for n=1..52.

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

Cf. A099634, A099635, A099636.

Sequence in context: A192322 A015708 A114822 * A274348 A143758 A101260

Adjacent sequences:  A099634 A099635 A099636 * A099638 A099639 A099640

KEYWORD

nonn

AUTHOR

Labos Elemer, Oct 28 2004

EXTENSIONS

More terms from Robert G. Wilson v, Nov 04 2004

STATUS

approved

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Last modified August 4 20:00 EDT 2020. Contains 336202 sequences. (Running on oeis4.)