A071144 Numbers n such that sum of distinct primes dividing n is divisible by the largest prime dividing n. Also n has exactly 5 distinct prime factors and n is squarefree.

3570, 8970, 10626, 15015, 16530, 20706, 24738, 24882, 36890, 38130, 44330, 49938, 51051, 52170, 54834, 55986, 59570, 62985, 68370, 73554, 74613, 77330, 79458, 81770, 87290, 91266, 96162, 96866, 103730, 106314, 116466, 123234, 128570, 129426, 129930, 138890

Offset: 1

Author

Labos Elemer, May 13 2002

Keywords

• nonn

Examples

			n = pqrst, p<q<r<s<t, primes, p+q+r+s+t = kt; n = 8970 = 2*3*5*13*23, sum = 46 = 2*23.
		

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], 5]&& !Equal[amo[n], 0], Print[{n, ba[n]}]], {n, 2, 1000000}]
sdpQ[n_]:=Module[{fi=FactorInteger[n][[;;,1]]},Length[fi]==5&&SquareFreeQ[n]&&Mod[Total[ fi],Max[fi]]==0]; Select[Range[150000],sdpQ] (* Harvey P. Dale, May 04 2023 *)

Formula

A008472(n)/A006530(n) is an integer; A001221(n) = 5, n is squarefree.