A133849 Least odd primitive abundant numbers with no factor 3 and with 5^n but not 5^(n+1) as a factor.

20169691981106018776756331, 33426748355, 5391411025, 26957055125, 134785275625, 673926378125, 3369631890625, 16848159453125, 84240797265625, 421203986328125, 2106019931640625, 10530099658203125, 52650498291015625, 263252491455078125, 1316262457275390625, 6581312286376953125

Offset: 0

Author

Pierre CAMI, Jan 06 2008

Keywords

• nonn

Comments

A subsequence of A115414, odd abundant numbers (A005231) not divisible by 3. The smallest of these equals a(2). All subsequent terms are a(n) = 5*a(n-1). - M. F. Hasler, Jul 28 2016

Examples

			a(0) = 20169691981106018776756331 = 5^0*7^2*11^2*13*17*19*23*29*31*37*41*43*47*53*59*61*67 = A047802(3), the least odd abundant number with no factor 3 or 5.
a(1) = 33426748355 = 5^1*7*11*13*17*19*23*29*31.
a(2) = 5391411025 = 5^2*7*11*13*17*19*23*29 = A115414(1) = A047802(2), the least odd abundant number with no factor 3.
		

Crossrefs

Cf. A115414, A005231, A005101.

Programs

PARI

A133849(n)=215656441*if(n>1,5^n,[3016998806898461,5][n+1]*31) \\ M. F. Hasler, Jul 28 2016

Formula

For all n >= 2, a(n) = 5^n*7*11*13*17*19*23*29. This can be seen from sigma[-1](5^n) = (5-1/5^n)/4 and sigma[-1](29#/5#) = 1.615... > 2/sigma[-1](5^n) for all n >= 2 (but not for n = 1), while sigma[-1](23#/5#) = 1.56... < 2*4/5 (and idem for any other factor omitted) is never large enough. - M. F. Hasler, Jul 28 2016

Extensions

Edited, a(3) corrected, and more terms added by M. F. Hasler, Jul 28 2016