A007368 -id:A007368 - cp's OEIS frontend

A300911 a(n) is the smallest positive integer k such that psi(x) = k has exactly n solutions, where psi(x) = A001615(x).

2, 1, 6, 84, 12, 24, 48, 168, 96, 72, 192, 144, 384, 672, 360, 960, 432, 288, 3648, 1080, 3600, 720, 2736, 1008, 576, 864, 11664, 6720, 7680, 1152, 7920, 6336, 2016, 1440, 3024, 1728, 2160, 14256, 5040, 2592, 2304, 13440, 9072, 10800, 43008, 26208, 24480, 4608, 2880, 10944, 6480

Offset: 0

Altug Alkan, Mar 15 2018

nonn

			a(3) = 84 because psi(2^2*13) = psi(5*13) = psi(83) = 84 and 84 is the least number with this property.

Cf. A001615, A007368, A007374.

psi[n_] := If[n == 1, 1, n Times @@ (1 + 1/First /@ FactorInteger@n)]; t = Sort[Reverse /@ Tally[Array[psi, 50000]]]; L = {2}; Do[ If[t[[j, 1]] == Length@ L, AppendTo[L, t[[j, 2]]]], {j, Length@t}]; L (* Giovanni Resta, Mar 16 2018 *)

{my(N=5*10^4, c=vectorsmall(N), i); A300911=List(); for(n=1,N,(i=A001615(n))>N||c[i]++); for(n=1,oo, for(i=1,N, c[i]==n && listput(A300911,i) && next(2)); break)} \\ M. F. Hasler, Mar 18 2018

A186273 a(n) is the least number k having exactly n representations as m + sigma(m), where sigma(m) is the sum of the divisors of m.

Original entry on oeis.org

2, 11, 95, 3623, 2363, 6143, 21263, 89303, 202703, 472973, 493763, 1013513, 3986483, 3306713, 2364863, 21283763, 19932413, 29391863, 74887313, 98679263, 87499913, 134797163, 201013313, 267843713, 560472413, 775337063, 361823963, 673985813

Offset: 1

J. M. Bergot, Feb 16 2011

nonn

			For the n-th term, the n solutions are
2     {1}
11    {4, 5}
95    {32, 39, 47}
3623  {1687, 1727, 1751, 1811}
2363  {1011, 1099, 1139, 1147, 1181}
6143  {2048, 2631, 2863, 2951, 2983, 3007}
21263 {9111, 10231, 10319, 10447, 10471, 10519, 10631}
89303 {38271, 41671, 42991, 43367, 44287, 44311, 44431, 44651}

Math Forum, Topic: Petaflop machine not required / n + sigma(n) [Broken link]

Cf. A007368 (smallest k such that sigma(x) = k has exactly n solutions).

nn=1000000; t=Table[n+DivisorSigma[1,n], {n, nn}]; t2=Select[t, # <= 2*nn+1&]; ts=Sort[Tally[t2]]; u=Union[Transpose[ts][[2]]]; c=Complement[Range[Max[u]], u]; If[c != {}, u=Range[c[[1]]-1]]; Table[Select[ts, #[[2]] == n &, 1][[1,1]], {n, u}]

Corrected and extended by T. D. Noe, Feb 16 2011

a(13)-a(28) from Donovan Johnson, Feb 17 2011

A258968 a(n) is the least positive integer x with A054973(x) = n and A258913(x) < x.

Original entry on oeis.org

2, 3, 124, 10714158

Offset: 0

Jeppe Stig Nielsen, Jun 15 2015

Is a(n) well-defined for all n?
For n > 1, a(n) belongs to sequence A258931.
The terms a(k), for 4 <= k <= 100, if they exist, are larger than 3*10^10. - Giovanni Resta, Jun 15 2015

			For n=2, sigma(x)=124 for x=48 and 75, and 48+75 = 123 < 124.
For n=3, sigma(x)=10714158 for x=3031200, 3417300, and 3987450; and their sum is 10435950 (<10714158).

Cf. A054973, A258913, A258931, A007368, A258914.

a(n)=x=0;while(x++,u=List();for(i=1,x,if(sigma(i)==x,listput(u,i)));if(#u==n&vecsum(Vec(u))

cp's OEIS Frontend

A300911 a(n) is the smallest positive integer k such that psi(x) = k has exactly n solutions, where psi(x) = A001615(x).

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A186273 a(n) is the least number k having exactly n representations as m + sigma(m), where sigma(m) is the sum of the divisors of m.

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A258968 a(n) is the least positive integer x with A054973(x) = n and A258913(x) < x.

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