A294649 -id:A294649 - cp's OEIS frontend

A297358 Numbers m such that the denominator of m/rho(m) is 3, where rho is A206369; i.e. A294649(m) = 3.

4, 14, 20, 84, 280, 672, 3360, 4200, 4214, 6160, 25284, 36960, 46200, 57792, 76160, 84280, 92400, 202272, 288960, 308700, 656640, 1011360, 1142400, 1264200, 1854160, 2469600, 3178560, 11124960, 12566400, 13906200, 22924160, 27812400, 107557632, 120165120, 212385600

Offset: 1

Michel Marcus, Dec 29 2017

nonn

The least instances for 4/3, 5/3, 7/3, 8/3, 10/3 and 11/3 are: 4, 20, 14, 672, 3360, 36960.

Then candidates for 13/3 and 14/3 are 54269201896764616671660406473798293913600000 and 23101697828019582727957348094429256309828763084415991060514234912131560924774400000000.

			4 is a term because 4/A206369(4) = 4/3.
14 is a term because 14/A206369(14) = 14/6 = 7/3.

Cf. A206369 (rho), A294649, A295236 (analog with 2 instead of 3).

Cf. A245775 (analog for sigma).

Select[Range[10^5], Denominator[#/(# DivisorSum[#, LiouvilleLambda[#]/# &])] == 3 &] (* Michael De Vlieger, Dec 29 2017 *)

rhope(p, e) = my(s=1); for(i=1, e, s=s*p + (-1)^i); s;
rho(n) = my(f=factor(n)); prod(i=1, #f~, rhope(f[i, 1], f[i, 2]));
isok(n) = denominator(n/rho(n))==3;

a(33)-a(35) from Jinyuan Wang, Feb 10 2020

A294650 a(n) = denominator(A206369(n))/n.

Original entry on oeis.org

1, 2, 3, 4, 5, 3, 7, 8, 9, 5, 11, 2, 13, 7, 15, 16, 17, 18, 19, 5, 7, 11, 23, 12, 25, 13, 27, 14, 29, 15, 31, 32, 33, 17, 35, 12, 37, 19, 13, 2, 41, 7, 43, 22, 45, 23, 47, 24, 49, 50, 51, 13, 53, 27, 11, 28, 19, 29, 59, 5, 61, 31, 3, 64, 65, 33, 67, 17, 69, 35

Offset: 1

Michel Marcus, Nov 06 2017

Michel Marcus, Table of n, a(n) for n = 1..10000
László Tóth, A survey of the alternating sum-of-divisors function, arXiv:1111.4842 [math.NT], 2011-2014.

Cf. A127724 (k-imperfect), A206369, A294649 (numerator).

A225680 is a subsequence (on squarefree indices). - Michel Marcus, Dec 22 2017

(* b = A209369 *) b[n_] := n*DivisorSum[n, LiouvilleLambda[#]/# &];
a[n_] := Denominator[b[n]/n];
Array[a, 100] (* Jean-François Alcover, Dec 04 2017 *)

rhope(p, e) = my(s=1); for(i=1, e, s=s*p + (-1)^i); s;
rho(n) = my(f=factor(n)); prod(i=1, #f~, rhope(f[i, 1], f[i, 2]));
a(n) = denominator(rho(n)/n);

cp's OEIS Frontend

A297358 Numbers m such that the denominator of m/rho(m) is 3, where rho is A206369; i.e. A294649(m) = 3.

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

Mathematica

PARI

Extensions