

A131902


Smallest positive integer k with the same sum of divisors as the nth integer for which such a k exists.


7



6, 14, 10, 14, 16, 20, 21, 33, 24, 28, 20, 30, 33, 30, 34, 30, 54, 40, 24, 42, 44, 42, 66, 30, 48, 42, 60, 57, 68, 44, 54, 40, 60, 66, 54, 52, 63, 85, 102, 74, 66, 104, 88, 66, 80, 60, 84, 99, 93, 96, 86, 114, 76, 132, 105, 102, 60, 88, 111, 90, 138, 105, 114, 102, 105, 138, 96
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OFFSET

1,1


LINKS

Robert Israel, Table of n, a(n) for n = 1..10000


FORMULA

Let S={n>0 : there exists a k>0 and k<n with sigma(k)=sigma(n)}. Then a(n):=min(k>0: sigma(k)=sigma(nth element of S)


EXAMPLE

a(3)=10 because 17 is the third integer for which a smaller integer with same sum of divisors exists and sigma(17)=1+17=18 and sigma(10)=1+2+5+10=18 and there is no k>0 less than 10 with sigma(k)=18


MAPLE

N:= 1000: # to use values of sigma <= N
V:= Vector(N): A:= Vector(N):
for n from 1 to N do
v:= numtheory:sigma(n);
if v <= N then
if V[v] = 0 then V[v]:= n
else A[n]:= V[v]
fi
fi
od:
subs(0=NULL, convert(A, list)); # Robert Israel, Mar 30 2018


MATHEMATICA

Clear[tmp]; Function[n, If[Head[ #1]===tmp, #1=n; Unevaluated[Sequence[]], #1]& [tmp[DivisorSigma[1, n]]]]/@Range[200]


CROSSREFS

Cf. A069822, A131903  A131908.
Sequence in context: A201449 A205300 A065938 * A265029 A329065 A184998
Adjacent sequences: A131899 A131900 A131901 * A131903 A131904 A131905


KEYWORD

easy,nonn


AUTHOR

Peter Pein (petsie(AT)dordos.net), Jul 26 2007


STATUS

approved



