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Search: id:A132630
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| A132630 |
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Numbers n such that sigma(n)-n divides sigma(n+1)-n-1, where sigma(n) is sum of positive divisors of n. |
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2
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| 2, 3, 5, 7, 9, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 85, 89, 97, 101, 103, 107, 109, 113, 125, 127, 131, 137, 139, 149, 151, 157, 163, 167, 169, 173, 179, 181, 191, 193, 197, 199
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Only odd numbers. All the prime numbers p are included because sigma(p)-p=1.
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EXAMPLE
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n=85 -> sigma(n+1)-n-1=1+2+43=46 sigma(n)-n=1+5+17=23 -> 46/23=2
n=125 -> sigma(n+1)-n-1=1+2+3+6+7+9+14+18+21+42+63=186 sigma(n)-n=1+5+25=31 -> 186/31=6
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MAPLE
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with(numtheory); P:=proc(n) local a, i; for i from 1 by 1 to n do if sigma(i)-i>0 then a:=(sigma(i+1)-i-1)/(sigma(i)-i); if a>0 and trunc(a)=a then print(i); fi; fi; od; end: P(200)
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CROSSREFS
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Cf. A132585, A132586, A132631.
Adjacent sequences: A132627 A132628 A132629 this_sequence A132631 A132632 A132633
Sequence in context: A065520 A090332 A136327 this_sequence A033946 A095415 A024678
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KEYWORD
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easy,nonn
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AUTHOR
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Paolo P. Lava & Giorgio Balzarotti (ppl(AT)spl.at), Aug 27 2007
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