A071145 Numbers n such that sum of distinct primes dividing n is divisible by the largest prime dividing n. Also n has exactly 6 distinct prime factors and n is squarefree.

72930, 106590, 190190, 222870, 335478, 397670, 620310, 836418, 844305, 884442, 1008678, 1195670, 1218945, 1247290, 1704794, 1761110, 1799798, 2086238, 2206022, 2328410, 2485830, 2496585, 2517258, 2863718, 2903538, 3024021, 3157665, 3172785, 3291890

Offset: 1

Author

Labos Elemer, May 13 2002

Keywords

• nonn

Examples

			n = pqrstw, p<q<r<s<t<w, primes, p+q+r+s+t+w = kt; n = 106590 = 2*3*5*11*17*19; sum = 2+3+5+11+17+19 = 57 = 3*19 (quotient=3) (Corrected Mar 06 2006.)
		

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], 6]&& !Equal[amo[n], 0], Print[{n, ba[n]}]], {n, 2, 1000000}]

Formula

A008472(n)/A006530(n) is an integer; A001221(n) = 6, n is squarefree.