A316100 Numbers k such that k is deficient but k+1 is abundant, that is, a deficient number followed by an abundant number.

11, 17, 19, 23, 29, 35, 39, 41, 47, 53, 55, 59, 65, 69, 71, 77, 79, 83, 87, 89, 95, 99, 101, 103, 107, 111, 113, 119, 125, 131, 137, 139, 143, 149, 155, 159, 161, 167, 173, 175, 179, 185, 191, 195, 197, 199, 203, 207, 209, 215, 219, 221, 223, 227, 233, 239

Offset

1,1

Links

Table of n, a(n) for n=1..56.

Example

11 is deficient and 12 is abundant.
17 is deficient and 18 is abundant.

Maple

with(numtheory):  select(n->sigma(n)<2*n and sigma(n+1)>2*(n+1), [$1..400]);

Mathematica

Select[Range@ 240, And[DivisorSigma[1, #] < 2 #, DivisorSigma[1, # + 1] > 2 (# + 1)] &] (* Michael De Vlieger, Jul 01 2018 *)

Prog

(GAP) Filtered([1..400], n->Sigma(n)<2*n and Sigma(n+1)>2*(n+1));
(PARI) isok(n) = (sigma(n) < 2*n) && (sigma(n+1) > 2*(n+1)); \\ Michel Marcus, Jul 02 2018

Crossrefs

Cf. A005100, A005101.

Sequence in context: A217063 A038966 A050778 * A049593 A216664 A019412

Adjacent sequences: A316097 A316098 A316099 * A316101 A316102 A316103

Keyword

nonn

Author

Muniru A Asiru, Jul 01 2018

Status

approved