A375462 a(1)=1; thereafter, if n is odd we require that a(n) be deficient and a(n) || a(n+1) abundant, otherwise a(n) abundant and a(n) || a(n+1) deficient. At each step, chose the smallest possible integer not yet in the sequence.

1, 12, 2, 20, 3, 18, 4, 40, 5, 60, 7, 36, 9, 24, 8, 70, 10, 56, 11, 48, 13, 30, 14, 72, 15, 42, 17, 80, 19, 84, 16, 96, 21, 54, 22, 88, 23, 100, 25, 90, 26, 104, 27, 66, 29, 112, 31, 108, 32, 120, 33, 78, 34, 132, 35, 140, 37, 156, 38, 144, 39, 102, 41, 160, 43

Offset

1,2

Links

Table of n, a(n) for n=1..65.

Example

a(1)=1 and n=1 is odd -> a(2)=12 because is the smallest abundant number not yet in the sequence such that a(1) || a(2) = 112 is abundant.
Now n=2 is even -> a(3)=2 because is the smallest deficient number not yet in the sequence such that a(2) || a(3) = 122 is deficient. And so on.

Maple

with(numtheory): P:=proc(q) local a, b, k, n; a:=[1];
for n from 2 to q do for k from 2 do if numboccur(k, a)=0
then b:=a[nops(a)]*10^length(k)+k;
if (n mod 2=0 and 2*b<sigma(b) and 2*k<sigma(k)) or
(n mod 2=1 and 2*b>sigma(b) and 2*k>sigma(k))
then a:=[op(a), k]; break; fi; fi; od; od; print(op(a)); end: P(65);

Crossrefs

Cf. A005100, A005101, A375417.

Sequence in context: A183729 A238718 A303782 * A335043 A360287 A040143

Adjacent sequences: A375459 A375460 A375461 * A375463 A375464 A375465

Keyword

nonn,base,easy

Author

Paolo P. Lava, Aug 17 2024

Status

approved