A247015 -id:A247015 - cp's OEIS frontend

A256440 Regular triangle where the n-th row lists the integers k between 1 and n ordered by increasing value of sigma(k)/k where sigma is the sum of divisors, A000203.

1, 1, 2, 1, 3, 2, 1, 3, 2, 4, 1, 5, 3, 2, 4, 1, 5, 3, 2, 4, 6, 1, 7, 5, 3, 2, 4, 6, 1, 7, 5, 3, 2, 4, 8, 6, 1, 7, 5, 3, 9, 2, 4, 8, 6, 1, 7, 5, 3, 9, 2, 4, 10, 8, 6, 1, 11, 7, 5, 3, 9, 2, 4, 10, 8, 6, 1, 11, 7, 5, 3, 9, 2, 4, 10, 8, 6, 12, 1, 13, 11, 7, 5, 3, 9, 2, 4, 10, 8, 6, 12

Offset: 1

Michel Marcus, Mar 29 2015

			Triangle starts:
1;
1, 2;
1, 3, 2;
1, 3, 2, 4;
1, 5, 3, 2, 4;
1, 5, 3, 2, 4, 6;
1, 7, 5, 3, 2, 4, 6;
...

Michel Marcus, Rows n = 1..100 of triangle, flattened
Michel Marcus, 100 rows

Cf. A000203, A247015, A247022.

f[n_] := Block[{t = Table[0, {n}], j, k}, For[j = 1, j <= n, j++, t[[j]] = {}; For[k = 1, k <= j, k++, AppendTo[t[[j]], DivisorSigma[1, k]/k]]]; Ordering /@ t]; f@ 13 // Flatten (* Michael De Vlieger, Mar 29 2015 *)

lista(nn) = {for (n=1, nn, v = vector(n, k, sigma(k)/k); w = vecsort(v,,1); for (k=1, n, print1(w[k], ", ")); print(););}

A247022 Integers m such that there is exactly one k < m with sigma(k)/k > sigma(m)/m, sigma(m) being the sum of the divisors of m.

Original entry on oeis.org

3, 8, 18, 30, 72, 168, 420, 3360, 7560, 12600, 20160, 30240, 32760, 50400, 65520, 83160, 131040, 221760, 831600, 1081080, 1663200, 1801800, 2882880, 6486480, 12252240, 24504480, 41081040, 43243200, 68468400, 82162080, 136936800, 205405200, 245044800, 410810400

Offset: 1

Michel Marcus, Sep 09 2014

nonn

Integers such that A247015(n) = 1.

			sigma(8)/8 is greater than all sigma(x)/x when x < 8 except 6; so 8 is here.

Cf. A000203 (sigma), A004394 (superabundant), A017665 and A017666 (sigma(n)/n).

Cf. A247015.

M1:= 3/2: M2:= 1: c1:= 1:
Res:= NULL: count:= 0:
for n from 3 while count < 20 do
  v:= numtheory:-sigma(n)/n;
  if v > M1 then M2:= M1; M1:= v; c1:= 1
  elif v = M1 then
     c1:= c1+1
  elif c1 = 1 and v >= M2 then
     M2:= v;
     Res:= Res,n: count:= count+1
  fi
od:
Res; # Robert Israel, Jul 28 2020

lista(nn) = {my(t=1, x=3/2, y); for(m=3, nn, if((g=sigma(m)/m)>x, t=1; y=x; x=g, if(g==x, t=0, if(g>=y&&t, y=g; print1(m, ", "))))); } \\ Jinyuan Wang, Jul 28 2020

a(15)-a(21) from Robert Israel, Jun 08 2018
Corrected and name changed by Robert Israel, Jul 28 2020
More terms from Jinyuan Wang, Jul 28 2020

A247034 Smallest integer x such that the number of integers y sigma(x)/x is exactly n.

Original entry on oeis.org

1, 3, 10, 5, 9, 7, 15, 32, 132, 11, 21, 13, 44, 70, 52, 17, 25, 19, 38, 33, 198, 23, 35, 46, 39, 76, 234, 29, 220, 31, 224, 62, 51, 136, 260, 37, 57, 55, 74, 41, 1170, 43, 196, 82, 69, 47, 10440, 154, 222, 94, 520, 53, 744, 148, 77, 190, 87, 59, 182, 61, 93

Offset: 0

Michel Marcus, Sep 10 2014

nonn

Conjecture: a(n) exists for all n.

Amiram Eldar, Table of n, a(n) for n = 0..421

Cf. A000203 (sigma), A004394 (superabundant), A017665 and A017666 (sigma(n)/n).

Cf. A247015.

lista(nn) = {v = vector(nn, n, sigma(n)/n); vmore = vector(nn+1); for (n=1, nn, nb = sum(i=1, n, v[i] > v[n]); if (vmore[nb+1] == 0, vmore[nb+1] = n);); for (i=1, #vmore, if (!vmore[i], break, print1(vmore[i], ", ")));}

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A256440 Regular triangle where the n-th row lists the integers k between 1 and n ordered by increasing value of sigma(k)/k where sigma is the sum of divisors, A000203.

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A247022 Integers m such that there is exactly one k < m with sigma(k)/k > sigma(m)/m, sigma(m) being the sum of the divisors of m.

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A247034 Smallest integer x such that the number of integers y sigma(x)/x is exactly n.

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