A103289 Numbers k such that both sigma(k) >= 2*k-1 and sigma(k+1) >= 2*(k+1)-1.

1, 4095, 5775, 5984, 7424, 11024, 21735, 21944, 26144, 27404, 39375, 43064, 49664, 56924, 58695, 61424, 69615, 70784, 76544, 77175, 79695, 81080, 81675, 82004, 84524, 84644, 89775, 91664, 98175, 103455, 104895, 106784, 109395, 111824

Offset: 1

Author

Max Alekseyev, Jan 28 2005

Keywords

• nonn

Comments

A004125(n) is less than A004125(n-1) and A004125(n+1) iff n belongs to A023196 but not to the current sequence.

Numbers k that both k and k+1 are in A103288.

Union of sequences A096399 and {2^m-1} for m in A103291.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..2500 from Muniru A Asiru)

Crossrefs

Cf. A103288, A096399, A103291, A004125, A023196.

Programs

GAP

Filtered([1..120000],n->Sigma(n)>=2*n-1 and Sigma(n+1)>2*(n+1)-1); # Muniru A Asiru, Jun 26 2018

Maple

with(numtheory): a:=`if`(sigma(n)>=2*n-1 and sigma(n+1)>=2*(n+1)-1,n,NULL): seq(a(n),n=1..120000); # Muniru A Asiru, Jun 26 2018

Mathematica

Select[Range[120000], And[DivisorSigma[1, #] >= 2 #1 - 1, DivisorSigma[1, # + 1] >= 2 (#1 + 1) - 1] &] (* Michael De Vlieger, Jun 29 2018 *)

PARI

for(i=1,1000000,if(sigma(i)>=2*i-1 && sigma(i+1)>=2*i+1, print1(i, ", ")));