cp's OEIS Frontend

A386317 Integers t which satisfy 3/2 <= abundancy(t) < 2 but which are not k-deficient-perfect numbers A331627.

%I A386317 #9 Jul 28 2025 18:54:58
%S A386317 14,22,26,34,38,46,58,62,68,74,76,82,86,92,94,98,106,110,116,118,122,
%T A386317 124,134,142,146,147,148,158,164,166,171,172,178,188,194,202,206,212,
%U A386317 214,218,225,226,236,242,244,248,254,255,262,268,274,278,284,285,286,292,296,298,302,314
%N A386317 Integers t which satisfy 3/2 <= abundancy(t) < 2 but which are not k-deficient-perfect numbers A331627.
%C A386317 A necessary (but not sufficient) condition for an integer t to be a k-deficient-m-perfect number: (m + 1)/2 <= abundancy(t) < m:
%C A386317 - for m = 2: 3/2 <= abundancy(t) < 2,
%C A386317 - for m = 3: 2 <= abundancy(t) < 3,
%C A386317 - for m = 4: 5/2 <= abundancy(t) < 4.
%e A386317 13 is not in this sequence because abundancy(13) = 14/13 (14/13 < 3/2).
%e A386317 14 is in this sequence because abundancy(14) = 12/7 (3/2 <= 12/7 < 2) but 14 is not a k-deficient-perfect number (therefore is not included in A331627).
%e A386317 15 is not in this sequence because abundancy(15) = 8/5 (3/2 <= 8/5 < 2) but 15 is a k-deficient-perfect number (therefore is included in A331627).
%o A386317 (Maxima)
%o A386317 (n:1, abundancy(x):=divsum(x)/x,
%o A386317      for t:1 thru 500 do
%o A386317         (if abundancy(t)>=3/2 and abundancy(t)<2 then
%o A386317         (A:append(args(powerset(delete(t,divisors(t)))),[{0}]), b:length(A),
%o A386317             for i:1 unless (divsum(t)+apply("+" , args(A[i])))/t=2 or i>=b do j:i,
%o A386317                if j>=b-1 then (print(n , "" , t), n:n+1))));
%o A386317 (PARI) isok(m) = my(d=divisors(m), ss=vecsum(d), ab=sigma(m)/m); if ((ab>=3/2) && (ab<2), d = Vec(d, #d-1); forsubset(#d, s, if (#s && (sum(i=1, #s, d[s[i]]) == 2*m - ss), return(0))); return(1)); \\ _Michel Marcus_, Jul 19 2025
%Y A386317 Cf. A000203, A271816, A331627.
%K A386317 nonn
%O A386317 1,1
%A A386317 _Lechoslaw Ratajczak_, Jul 18 2025