A112644 - OEIS

%I #21 Aug 16 2024 08:37:42

%S 22309287,28129101,30069039,34051017,35888853,36399363,38057019,

%T 39768729,40681641,41708667,43444401,45588543,45894849,48141093,

%U 48555507,50489439,51294243,51408357,53804751,54777723,55186131,56429373,57228171,58555497,59168109

%N Odd and squarefree abundant numbers not divisible by 5.

%C The least term that is not divisible by 3 is 73#/5# = Product_{k=4..21} prime(k) = 1357656019974967471687377449. - _Amiram Eldar_, Aug 15 2024

%H Donovan Johnson, <a href="/A112644/b112644.txt">Table of n, a(n) for n = 1..1000</a>

%e 99906807 = 3*7*11*13*17*19*103 is a term since it is an odd squarefree number that is not divisible by 5, and sigma(99906807) = 201277440 > 2*99906807.

%t ta={{0}};Do[g=n;s=DivisorSigma[1, n]-2*n; If[Greater[s, 0]&&Equal[Abs[MoebiusMu[n]], 1]&& !Equal[Mod[n, 2], 0]&&!Equal[Mod[n, 5], 0], Print[n, PrimeFactorList[n], s];ta=Append[ta, n]], {n, 10000000, 100000000}];{ta=Delete[ta, 1], g}

%o (PARI) issfab(k) = my(f = factor(k)); issquarefree(f) && sigma(f, -1) > 2;

%o is(k) = gcd(k, 10) == 1 && issfab(k); \\ _Amiram Eldar_, Aug 15 2024

%Y Cf. A087248, A046391, A112643, A112642, A112640.

%Y Cf. A005231, A047802.

%K nonn

%O 1,1

%A _Labos Elemer_, Sep 20 2005