cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A045613 Minimal elements of pairs of "Super Unitary Amicable Numbers", sorted by their minimal elements.

Original entry on oeis.org

33, 105, 110, 208, 268, 455, 695, 812, 1609, 1808, 1892, 1913, 2096, 2145, 3123, 3272, 3867, 4129, 5424, 5600, 5916, 6524, 6783, 7069, 7119, 7875, 9716, 10506, 11088, 11265, 11552, 12324, 12892, 12939, 13712, 14210, 15429, 15762, 17252, 17490, 18368, 19616
Offset: 1

Views

Author

Yasutoshi Kohmoto

Keywords

Links

Crossrefs

Cf. A045614, A034448.

Programs

  • Mathematica
    usigma[n_] := If[n == 1, 1, Times @@ (1 + Power @@@ FactorInteger[n])]; u[n_] := usigma[usigma[n]] - n; s = {}; Do[m = u[n]; If[m > n && u[m] == n, AppendTo[s, n]], {n, 1, 10000}]; s (* Amiram Eldar, Feb 18 2019 *)

Formula

usigma(usigma(a)) = usigma(usigma(b)) = a+b where aA034448(n) is the sum of the unitary divisors of n. This sequence gives the values of a; A045614 gives the values of b.

Extensions

Edited by Dean Hickerson, Nov 06 2006
Offset corrected by Donovan Johnson, Jul 26 2012
More terms from Amiram Eldar, Feb 18 2019

A324256 Larger of super amicable pair m < n defined by sigma(sigma(m)) = sigma(sigma(n)) = m + n.

Original entry on oeis.org

37, 28201, 34687, 65587, 2089951, 4091797, 8340613, 8161477, 10124833, 18927067, 37179433, 37393633, 25855567, 64346413, 107160373, 95150203, 159440893, 238973101, 257658061, 277743397, 322210813, 256268149, 349883707, 578403913, 814865497, 752724457, 704710543
Offset: 1

Views

Author

Amiram Eldar, Feb 19 2019

Keywords

Comments

The terms are ordered according to the their lesser counterparts (A324255).
Analogous to A002046 as A019279 is analogous to A000396.

Examples

			(23, 37) are the first pair since sigma(sigma(23)) = sigma(sigma(37)) = 60 = 23 + 37.

Crossrefs

Cf. A000203, A000396, A002046, A019279, A045614 (unitary analog), A051027, A324255.

Programs

  • Mathematica
    seq={}; s[n_]:=DivisorSigma[1,DivisorSigma[1,n]]-n; Do[m=s[n];If[m>n && s[m]==n, AppendTo[seq, m]], {n,1,60000}]; seq
  • PARI
    f(n) = sigma(sigma(n)) - n;
lista(nn) = {for (n=1, nn, my(fn = f(n)); if ((fn > n) && (f(fn) == n), print1(fn, ", ")););} \\ Michel Marcus, Feb 20 2019

A126163 Number of super unitary amicable pairs (i,j) with i

Original entry on oeis.org

0, 1, 8, 27, 102, 375, 1134, 3589, 11942, 40410
Offset: 1

Views

Author

Ant King, Dec 20 2006

Keywords

Examples

			a(6)=375 because there are 375 super unitary (m,n) pairs with m<n and for which m<=10^6

Links

Crossrefs

Cf. A045613, A045614.

Programs

  • Mathematica
    UnitaryDivisors[n_Integer?Positive] := Select[Divisors[n], GCD[ #, n/# ] == 1 \ &];
UnitaryDivisorSum[n_Integer?Positive] := Plus @@ UnitaryDivisors[n];
f[ k_] := Nest[UnitaryDivisorSum, k, 2] - k;
g[ k_] := Nest[UnitaryDivisorSum, f[k], 2] - f[k];
m = 10^7;
data1 = Select[Range[m], g[ # ] == # &];
data2 = Nest[UnitaryDivisorSum, #, 2] - # & /@ data1;
data3 = Table[{data1[[k]], data2[[k]]}, {k, 1, Length[data1]}];
data4 = DeleteCases[Table[If[Nest[UnitaryDivisorSum, First[data3[[k]]], 2] == Nest[UnitaryDivisorSum, Last[data3[[k]]], 2] \ && ! First[data3[[k]]] >= Last[data3[[k]]], data3[[k]], 0], {k, 1, Length[data3]}], 0];
data5 = Table[Length[Select[data4, First[ # ] < 10^k \ &]], {k, 1, 7}]

Formula

Integer pairs (m,n) with m

Extensions

a(8)-a(10) from Amiram Eldar, Feb 18 2019
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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