A071146 Numbers n such that sum of distinct primes dividing n is divisible by the largest prime dividing n. Also n has exactly 7 distinct prime factors and n is squarefree.

1231230, 2062830, 2181270, 3327870, 3594990, 4224990, 4320030, 4671030, 5162430, 5411406, 5414430, 6767670, 7052430, 7432230, 7870830, 7947030, 8150142, 8273265, 8287230, 8569470, 8804334, 9378390, 10630830, 10705695, 10757838, 10776990, 10900230

Offset: 1

Author

Labos Elemer, May 13 2002

Keywords

• nonn

Examples

			n = pqrstu, p<q<r<s<t<u, primes, p+q+r+s+t+u = ku; n = 9378390 = 2*3*5*7*17*37*71; sum = 2+3+5+7+17+37+71 = 142 = 2*71
		

Links

• Donovan Johnson, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A008472, A006530, A000961, A025475, A037074, A071139-A071147.

Programs

Mathematica

ffi[x_] := Flatten[FactorInteger[x]] lf[x_] := Length[FactorInteger[x]] ba[x_] := Table[Part[ffi[x], 2*w-1], {w, 1, lf[x]}] sb[x_] := Apply[Plus, ba[x]] ma[x_] := Part[Reverse[Flatten[FactorInteger[x]]], 2] amo[x_] := Abs[MoebiusMu[x]] Do[s=sb[n]/ma[n]; If[IntegerQ[s]&&Equal[lf[n], 7]&& !Equal[amo[n], 0], Print[{n, ba[n]}]], {n, 2, 1000000}]

Formula

A008472(n)/A006530(n) is an integer; A001221(n) = 7, n is squarefree.