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.

Previous Showing 11-14 of 14 results.

A371420 Greater member of Carmichael's variant of amicable pair: numbers k < m such that s(k) = m and s(m) = k, where s(k) = A371418(k).

Original entry on oeis.org

14, 62, 124, 189, 254, 508, 2032, 16382, 32764, 131056, 262142, 524284, 524224, 1048574, 2097148, 2097136, 8388592, 8388544, 33554368, 536866816, 2147479552, 4294967294, 8589934588, 34359738352, 34359672832, 137438953408
Offset: 1

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Author

Amiram Eldar, Mar 23 2024

Keywords

Comments

The terms are ordered according to their lesser counterparts (A371419).

Examples

			14 is a term since A371418(14) = 12 < 14, and A371418(12) = 14.
		

Crossrefs

Programs

  • Mathematica
    r[n_] := n/FactorInteger[n][[1, 1]]; s[n_] := r[DivisorSigma[1, n]]; seq = {}; Do[m = s[n]; If[m > n && s[m] == n, AppendTo[seq, m]], {n, 1, 10^6}]; seq
  • PARI
    f(n) = {my(s = sigma(n)); if(s == 1, 1, s/factor(s)[1, 1]);}
    lista(nmax) = {my(m); for(n = 1, nmax, m = f(n); if(m > n && f(m) == n, print1(m, ", ")));}

A348603 Larger member of a nonexponential amicable pair: numbers (k, m) such that nesigma(k) = m and nesigma(m) = k, where nesigma(k) is the sum of the nonexponential divisors of k (A160135).

Original entry on oeis.org

204, 19332, 168730, 1099390, 1292570, 1598470, 2062570, 2429030, 3077354, 3903012, 4488910, 6135962, 5504110, 5812130, 7158710, 8221598, 9627915, 10893230, 10043690, 11049730, 10273670, 18087818, 19150222, 17578785, 23030090, 32174506, 35997346, 40117714, 39944086
Offset: 1

Views

Author

Amiram Eldar, Oct 25 2021

Keywords

Comments

The terms are ordered according to their smaller counterparts (A348602).

Examples

			204 is a term since A160135(204) = 198 and A160135(198) = 204.
		

Crossrefs

Programs

  • Mathematica
    esigma[n_] := Times @@ (Sum[First[#]^d, {d, Divisors[Last[#]]}] &) /@ FactorInteger[n]; s[n_] := DivisorSigma[1, n] - esigma[n]; seq = {}; Do[m = s[n]; If[m > n && s[m] == n, AppendTo[seq, m]], {n, 1, 1.7*10^6}]; seq

A292019 List of pairs of unitary amicable numbers (m, n) with record value of m/n.

Original entry on oeis.org

114, 126, 44772, 49308, 241110, 242730, 10254970, 10273670, 766292835, 766512285, 17454440640, 17454615360
Offset: 1

Views

Author

Amiram Eldar, Sep 07 2017

Keywords

Comments

The 2 members in each pair are adjacent to each other in the sequence.
The unitary version of A287026.

Examples

			The ratios m/n are
114/126 = 0.90476...
44772/49308 = 0.90800...
241110/242730 = 0.99332...
10254970/10273670 = 0.99818...
766292835/766512285 = 0.99971...
17454440640/17454615360 = 0.99999...
		

Crossrefs

A292020 List of pairs of unitary amicable numbers (m, n) with record low values of m/n.

Original entry on oeis.org

114, 126, 18018, 22302, 32130, 40446, 197340, 286500, 703972667580, 1057831128900
Offset: 1

Views

Author

Amiram Eldar, Sep 07 2017

Keywords

Comments

The 2 members in each pair are adjacent to each other in the sequence.
The unitary version of A287011.

Examples

			The ratios m/n are
114/126 = 0.904...
18018/22302 = 0.807...
32130/40446 = 0.794...
197340/286500 = 0.688...
703972667580/1057831128900 = 0.665...
		

Crossrefs

Previous Showing 11-14 of 14 results.