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Search: id:A117553
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| A117553 |
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When adding some positive divisors of n in order from lowest divisor to highest divisor, a(n) is lowest sum achievable which is >= n. |
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+0
4
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| 1, 3, 4, 7, 6, 6, 8, 15, 13, 18, 12, 16, 14, 24, 24, 31, 18, 21, 20, 22, 32, 36, 24, 24, 31, 42, 40, 28, 30, 42, 32, 63, 48, 54, 48, 37, 38, 60, 56, 50, 42, 54, 44, 84, 78, 72, 48, 52, 57, 93, 72, 98, 54, 66, 72, 64, 80, 90, 60, 78, 62, 96, 104, 127, 84, 78, 68, 126, 96, 74, 72
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Often, but not always, a(n)=n+A054024(n). The exceptions to this rule are at n=24, 36, 48, 60, 72, 84,90, 96, 108,... - R. J. Mathar (mathar(AT)strw.leideuniv.nl), Mar 14 2007
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EXAMPLE
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12's divisors are 1,2,3,4,6, and 12. Adding the divisors in order we have:
1 = 1, 1+2 = 3, 1+2+3 = 6, 1+2+3+4 = 10, 1+2+3+4+6 = 16, and 1+2+3+4+6+12 = 28.
Of these sums, 1+2+3+4+6 = 16 is the lowest which is >= 12. So a(12) = 16.
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MAPLE
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A117553 := proc(n) local divs, a, i ; divs := numtheory[divisors](n) ; a := op(1, divs) ; i := 1 ; while a < n do i := i+1 ; a := a+op(i, divs) ; od ; RETURN(a) ; end: for n from 1 to 80 do printf("%d, ", A117553(n)) ; od ; - R. J. Mathar (mathar(AT)strw.leideuniv.nl), Mar 14 2007
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CROSSREFS
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Cf. A117552, A125746, A125747.
Sequence in context: A067342 A105827 A023888 this_sequence A120224 A132009 A086455
Adjacent sequences: A117550 A117551 A117552 this_sequence A117554 A117555 A117556
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KEYWORD
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nonn
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AUTHOR
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Leroy Quet (qq-quet(AT)mindspring.com), Mar 28 2006
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EXTENSIONS
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More terms from R. J. Mathar (mathar(AT)strw.leideuniv.nl), Mar 14 2007
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