OFFSET
1,1
COMMENTS
Apparently these numbers come up mostly by pairs m, m+3 with m even; the odd terms being a subsequence of A005231. But this is not always the case (e.g., note the term 7425).
The numbers of terms not exceeding 10^k, for k = 3, 4, ..., are 2, 43, 393, 3635, 37599, 374092, 3731903, 37338208, 373256850, ... . Apparently, the asymptotic density of this sequence exists and equals 0.00373... . - Amiram Eldar, May 30 2023
LINKS
Muniru A Asiru, Table of n, a(n) for n = 1..10000
EXAMPLE
942 is abundant, 943 and 944 are deficient, 945 is abundant.
945 is abundant, 946 and 947 are deficient, 948 is abundant.
MAPLE
with(numtheory): select(n->sigma(n)>2*n and sigma(n+1)<2*(n+1) and sigma(n+2)<2*(n+2) and sigma(n+3)>2*(n+3), [$1..12000]); # Muniru A Asiru, Jun 09 2018
MATHEMATICA
With[{abs = Select[Range[10000], DivisorSigma[-1, #] > 2 &]}, abs[[Position[Differences[abs], 3] // Flatten]]] (* Amiram Eldar, May 30 2023 *)
SequencePosition[Table[If[DivisorSigma[1, n]>2n, 1, 0], {n, 10000}], {1, 0, 0, 1}][[;; , 1]] (* Harvey P. Dale, Aug 31 2024 *)
PROG
(PARI) isok(n) = (sigma(n)> 2*n) && (sigma(n+1)< 2*(n+1)) && (sigma(n+2) < 2*(n+2)) && (sigma(n+3) > 2*(n+3)); \\ Michel Marcus, Aug 21 2013
(GAP) a:=Filtered([1..130000], n->Sigma(n)>2*n and Sigma(n+1)<2*(n+1) and Sigma(n+2)<2*(n+2) and Sigma(n+3)>2*(n+3)); # Muniru A Asiru, Jun 09 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
Michel Marcus, Aug 21 2013
STATUS
approved