A112640 Odd abundant numbers divisible neither by 5 nor 7.

28683369, 36165987, 38660193, 86050107, 108497961, 115980579, 131339637, 138428433, 140397543, 153393669, 160876287, 258150321, 277272567, 296394813, 315517059, 325493883, 347941737, 353761551, 372883797, 373715199, 392006043

Offset: 1

Author

Labos Elemer, Sep 15 2005

Keywords

• nonn

Comments

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

From Amiram Eldar, Aug 15 2024: (Start)

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

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

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..500 from Zak Seidov)
• Carlos Rivera, Puzzle 329. Odd abundant numbers not divided by 2 or 3, The Prime Puzzles and Problems Connection.

Crossrefs

Cf. A005231, A047802, A064001, A110585.

Programs

Mathematica

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 *)

PARI

is(n)=gcd(n,70)==1 && sigma(n,-1)>2 \\ Charles R Greathouse IV, Feb 21 2017

Extensions

Extended by Ray Chandler, Sep 19 2005