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A133849 Least odd primitive abundant numbers with no factor 3 and with 5^n but not 5^(n+1) as a factor. 1
20169691981106018776756331, 33426748355, 5391411025, 26957055125, 134785275625, 673926378125, 3369631890625, 16848159453125, 84240797265625, 421203986328125, 2106019931640625, 10530099658203125, 52650498291015625, 263252491455078125, 1316262457275390625, 6581312286376953125 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

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

LINKS

Table of n, a(n) for n=0..15.

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

EXAMPLE

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.

PROG

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

CROSSREFS

Cf. A115414, A005231, A005101.

Sequence in context: A009190 A095444 A217416 * A281907 A246288 A246255

Adjacent sequences:  A133846 A133847 A133848 * A133850 A133851 A133852

KEYWORD

nonn

AUTHOR

Pierre CAMI, Jan 06 2008

EXTENSIONS

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

STATUS

approved

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Last modified October 15 05:56 EDT 2018. Contains 316202 sequences. (Running on oeis4.)