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A071140 Numbers n such that sum of distinct primes dividing n is divisible by largest prime dividing n; n is neither a prime, nor a true power of prime. 6
30, 60, 70, 90, 120, 140, 150, 180, 240, 270, 280, 286, 300, 350, 360, 450, 480, 490, 540, 560, 572, 600, 646, 700, 720, 750, 810, 900, 960, 980, 1080, 1120, 1144, 1200, 1292, 1350, 1400, 1440, 1500, 1620, 1750, 1798, 1800, 1920, 1960, 2160, 2240, 2250 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

a(n) are the numbers such that the difference between the largest and the smallest prime divisor equals the sum of the other distinct prime divisors. - Michel Lagneau, Nov 13 2011

The statement above is only true for 966 of the first 1000 terms. The first counterexample is a(140) = 15015. - Donovan Johnson, Apr 10 2013

Lagneau's definition can be simplified to the largest prime divisor equals the sum of the other distinct prime divisors. - Christian N. K. Anderson, Apr 15 2013

LINKS

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

FORMULA

A008472(n)/A006530(n) is integer and n has at least 3 distinct prime factors.

A008472(a(n)) mod A006530(a(n)) = 0 and A010055(a(n)) = 0. - Reinhard Zumkeller, Apr 18 2013

EXAMPLE

n = 70 = 2*5*7 has a form of 2pq, where p and q are twin primes; n = 3135 = 3*5*11*19, sum = 3+5+11+19 = 38 = 2*19, divisible by 19.

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] Do[s=sb[n]/ma[n]; If[IntegerQ[s]&&Greater[s, 1], Print[{n, ba[n]}]], {n, 2, 1000000}]

(* Second program: *)

Select[Range@ 2250, And[Length@ # > 1, Divisible[Total@ #, Last@ #]] &[FactorInteger[#][[All, 1]] ] &] (* Michael De Vlieger, Jul 18 2017 *)

PROG

(Haskell)

a071140 n = a071140_list !! (n-1)

a071140_list = filter (\x -> a008472 x `mod` a006530 x == 0) a024619_list

-- Reinhard Zumkeller, Apr 18 2013

CROSSREFS

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

Subsequence of A024619.

Sequence in context: A066031 A212666 A291046 * A221054 A074915 A073461

Adjacent sequences:  A071137 A071138 A071139 * A071141 A071142 A071143

KEYWORD

nonn

AUTHOR

Labos Elemer, May 13 2002

STATUS

approved

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Last modified April 10 08:09 EDT 2021. Contains 342845 sequences. (Running on oeis4.)