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Odd abundant numbers divisible neither by 5 nor 7.
6

%I #28 Aug 16 2024 08:37:47

%S 28683369,36165987,38660193,86050107,108497961,115980579,131339637,

%T 138428433,140397543,153393669,160876287,258150321,277272567,

%U 296394813,315517059,325493883,347941737,353761551,372883797,373715199,392006043

%N Odd abundant numbers divisible neither by 5 nor 7.

%C Subsequence of A064001 which itself is a subsequence of A005231. All 500 terms in b-file are divisible by 99. Cf. also A047802. - _Zak Seidov_, Mar 30 2011

%C From _Amiram Eldar_, Aug 15 2024: (Start)

%C The least term that is not divisible by 99 is a(1718) = 21097921689.

%C The least term that is not divisible by 3 is 149#/7# = Product_{k=5..35} prime(k) = 7105630242567996762185122555313528897845637444413640621. (End)

%H Amiram Eldar, <a href="/A112640/b112640.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..500 from Zak Seidov)

%H Carlos Rivera, <a href="http://www.primepuzzles.net/puzzles/puzz_329.htm">Puzzle 329. Odd abundant numbers not divided by 2 or 3</a>, The Prime Puzzles and Problems Connection.

%t Do[If[Mod[n,5]>0&&Mod[n,7]>0&&DivisorSigma[1, n]>2n, Print[n]], {n, 28683369, 6*10^9,2}] (* _Zak Seidov_, Mar 30 2011 *)

%o (PARI) is(n)=gcd(n,70)==1 && sigma(n,-1)>2 \\ _Charles R Greathouse IV_, Feb 21 2017

%Y Cf. A005231, A047802, A064001, A110585.

%K nonn

%O 1,1

%A _Labos Elemer_, Sep 15 2005

%E Extended by _Ray Chandler_, Sep 19 2005