A112644 Odd and squarefree abundant numbers not divisible by 5.

22309287, 28129101, 30069039, 34051017, 35888853, 36399363, 38057019, 39768729, 40681641, 41708667, 43444401, 45588543, 45894849, 48141093, 48555507, 50489439, 51294243, 51408357, 53804751, 54777723, 55186131, 56429373, 57228171, 58555497, 59168109

Offset: 1

Author

Labos Elemer, Sep 20 2005

Keywords

• nonn

Comments

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

Examples

			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.
		

Links

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

Crossrefs

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

Cf. A005231, A047802.

Programs

Mathematica

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}

PARI

issfab(k) = my(f = factor(k)); issquarefree(f) && sigma(f, -1) > 2;
is(k) = gcd(k, 10) == 1 && issfab(k); \\ Amiram Eldar, Aug 15 2024