A133849 - OEIS

%I #12 Jul 28 2016 22:38:45

%S 20169691981106018776756331,33426748355,5391411025,26957055125,

%T 134785275625,673926378125,3369631890625,16848159453125,

%U 84240797265625,421203986328125,2106019931640625,10530099658203125,52650498291015625,263252491455078125,1316262457275390625,6581312286376953125

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

%C 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

%F 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

%e 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.

%e a(1) = 33426748355 = 5^1*7*11*13*17*19*23*29*31.

%e 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.

%o (PARI) A133849(n)=215656441*if(n>1,5^n,[3016998806898461,5][n+1]*31) \\ _M. F. Hasler_, Jul 28 2016

%Y Cf. A115414, A005231, A005101.

%K nonn

%O 0,1

%A _Pierre CAMI_, Jan 06 2008

%E Edited, a(3) corrected, and more terms added by _M. F. Hasler_, Jul 28 2016