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Search: id:A110928
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| A110928 |
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Pairs of distinct numbers m and n, m<n, such that sigma_2(m)=sigma_2(n), where sigma_2(n) is the sum of the squares of all divisors of n. |
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+0
1
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| 6, 7, 24, 26, 30, 35, 40, 47, 66, 77, 78, 91, 102, 119, 114, 133, 120, 130, 120, 141, 130, 141, 136, 157, 138, 161, 150, 175, 168, 182, 174, 203, 186, 215, 186, 217, 215, 217, 222, 259, 230, 249, 246, 287, 258, 301, 264, 286, 280, 282, 280, 329, 282, 329, 318
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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There do not appear to be any pairs (m,n) such that sigma_k(m)=sigma_k(n) for k>2.
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FORMULA
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sigma_2(m)=sigma_2(n), m<n
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EXAMPLE
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sigma_2(30)=1^1+2^2+3^2+5^2+6^2+10^2+15^2+30^2=1300 and sigma_2(35)=1^2+5^2+7^2+35^2=1300.
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MAPLE
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with(numtheory); sigmap := proc(p, n) convert(map(proc(z) z^p end, divisors(n)), `+`) end; SA2:=[]: for z from 1 to 1 do for m to 1500 do M:=sigmap(2, m); for n from m+1 to 1500 do N:=sigmap(2, n); if N=M then SA2:=[op(SA2), [m, n, N]] fi od od od; SA2; select(proc(z) z[1]<=1000 end, SA2); #just to shorten it a bit
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CROSSREFS
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Cf. A001157, A002025, A002046, A063990.
Sequence in context: A048062 A081284 A099572 this_sequence A067151 A135987 A054289
Adjacent sequences: A110925 A110926 A110927 this_sequence A110929 A110930 A110931
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KEYWORD
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nonn
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AUTHOR
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Walter A. Kehowski (wkehowski(AT)cox.net), Sep 23 2005
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