A131905 -id:A131905 - cp's OEIS frontend

A131902 Smallest positive integer k with the same sum of divisors as the n-th integer for which such a k exists.

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

Offset: 1

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

			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.

Robert Israel, Table of n, a(n) for n = 1..10000
Max Alekseyev, PARI/GP Scripts for Miscellaneous Math Problems (invphi.gp).

Cf. A069822, A131903, A131904, A131905, A131906, A131907, A131908.

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

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

list(lim) = my(m); for(k = 1, lim, m = invsigmaMin(sigma(k)); if(m < k, print1(m, ", "))); \\ Amiram Eldar, Dec 20 2024, using Max Alekseyev's invphi.gp

Let S = {n>0 : there exists a k>0 and k0: sigma(k) = sigma(n-th element of S)).

A131906 Smallest positive integer k with the same sum of squares of divisors as the n-th integer for which such a k exists.

Original entry on oeis.org

6, 24, 30, 40, 66, 78, 102, 120, 114, 120, 136, 138, 150, 168, 174, 186, 186, 230, 222, 280, 264, 246, 258, 280, 318, 330, 354, 360, 366, 430, 408, 390, 402, 408, 456, 426, 438, 440, 474, 498, 510, 552, 520, 534, 600, 645, 570, 582, 606, 618, 642, 696, 654, 680

Offset: 1

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

			a(5)=66 because A131905(5)=77 and the sum of the squares of the divisors of 77 is 1+49+121+5929=6100 and the sum of the squares of the divisors of 66 is 1+4+9+36+121+484+1089+4356=6100 and there is no smaller positive integer with this squaresum of its divisors

Cf. A069822, A131902-A131908.

Clear[tmp]; Last@Transpose[ Function[n, (If[Head[ #1] === tmp, #1 = n; Unevaluated[Sequence[]], {n, #1}] & )[tmp[DivisorSigma[2, n]]]] /@ Range[500]]

lista(nn) = {for (n=1, nn, my(sn = sigma(n,2)); for (k=1, n-1, if (sigma(k, 2) == sn, print1(k, ", "); break);););} \\ Michel Marcus, Apr 03 2015

a(n)=min(k>0, k has the same sum of squares of divisors as A131905(n))

More terms from Michel Marcus, Apr 03 2015

cp's OEIS Frontend

A131902 Smallest positive integer k with the same sum of divisors as the n-th integer for which such a k exists.

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