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Search: id:A159907
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| A159907 |
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Numbers n with half-integral abundancy index, sigma(n)/n = k+1/2 with integer k. |
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6
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| 2, 24, 4320, 4680, 26208, 8910720, 17428320, 20427264, 91963648, 197064960, 8583644160, 10200236032, 21857648640, 57575890944, 57629644800, 206166804480, 17116004505600, 1416963251404800, 15338300494970880
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OFFSET
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1,1
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COMMENT
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Obviously, all a(k) must be even (cf. formula), but e.g. a(9) and a(12) are not divisible by 3. See A007691 for numbers with integral abundancy.
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LINKS
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Walter Nissen, Abundancy : Some Resources
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FORMULA
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A159907 = { n | 2*A000203(n) is in n*A005408 } = { n | A054024(n) = n/2 }
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EXAMPLE
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a(1) = 2 since sigma(2)/2 = (1+2)/2 = 3/2 is of the form k+1/2 with integer k=1.
Odd numbers and higher powers of 2 cannot be in the sequence; 6 is in A000396 and thus in A007691, and n=10,12,14,18,20,22 don't have integral 2*sigma(n)/n.
a(2) = 24 is in the sequence since sigma(24)/24 = (1+2+3+4+6+8+12+24)/24 = (24+12+24)/24 = k+1/2 with integer k=2.
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CROSSREFS
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Cf. A000203, A088912, A141643 (k=2), A055153 (k=3), A141645 (k=4), A159271 (k=5).
Adjacent sequences: A159904 A159905 A159906 this_sequence A159908 A159909 A159910
Sequence in context: A111430 A059332 A000794 this_sequence A088912 A055462 A088600
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KEYWORD
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nonn
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AUTHOR
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M. F. Hasler (MHasler(AT)univ-ag.fr), Apr 25 2009
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