A383398 -id:A383398 - cp's OEIS frontend

A383399 For n>1, a(n) is the smallest number greater than a(n-1), whose sum with any previous term is deficient, with a(1) = 1.

1, 2, 3, 6, 7, 8, 31, 43, 44, 91, 115, 121, 122, 127, 128, 140, 146, 163, 211, 248, 283, 290, 331, 403, 427, 464, 511, 595, 631, 667, 668, 751, 842, 883, 931, 955, 1051, 1106, 1123, 1171, 1243, 1291, 1388, 1411, 1555, 1591, 1682, 1711, 1723, 1771, 1843, 1891, 2011, 2131

Offset: 1

Jakub Buczak, Apr 25 2025

nonn

If not for the set condition that a(n) must be greater than a(n-1), the sequence would consist of only 1's, because 2 is a deficient number.
While a majority of the terms are deficient, a few are abundant, with the first instance being a(16) = 140.
This is also equivalent to the sum of any 2 terms being a deficient number.

			7 is a member, because 7+6, 7+3, 7+2 and 7+1 are all deficient.

Jakub Buczak, Table of n, a(n) for n = 1..10000

Cf. A383398, A005101, A005100.

q:= n-> is(numtheory[sigma](n)<2*n):
a:= proc(n) option remember; local k, l;
      l:= [seq(a(i), i=1..n-1)]:
      for k from 1+`if`(n>1, a(n-1), 0)
        while not andmap(j-> q(k+j), l) do od; k
    end:
seq(a(n), n=1..54);  # Alois P. Heinz, Apr 25 2025

a[1] = 1; a[n_] := a[n] = Module[{k = a[n-1] + 1}, While[AnyTrue[Array[a, n-1], DivisorSigma[-1, #+k] >= 2 &], k++]; k]; Array[a, 54] (* Amiram Eldar, Apr 26 2025 *)

isdeficient(n) = (sigma(n) < 2*n) ;
isok(k, n, va) = for (i=1, n-1, if (! isdeficient(k+va[i]), return(0));); return(1);
lista(nn) = my(va=vector(nn)); for (n=1, nn, my(k=if (n==1, 1, 1+va[n-1])); while(! isok(k, n, va), k++); k; va[n] = k;); va; \\ Michel Marcus, Apr 26 2025

cp's OEIS Frontend

A383399 For n>1, a(n) is the smallest number greater than a(n-1), whose sum with any previous term is deficient, with a(1) = 1.

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