This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A372742 #13 May 07 2025 12:20:04
%S A372742 2,3,5,7,11,12,13,17,18,19,23,24,29,31,36,37,41,43,47,53,56,59,61,67,
%T A372742 71,73,79,80,83,84,89,96,97,98,101,103,107,109,112,113,127,131,135,
%U A372742 137,139,140,149,150,151,156,157,163,167,173,179,181,191,193,197,198
%N A372742 Numbers k such that there is a unique number m for which the sum of the aliquot coreful divisors of m (A336563) is k.
%C A372742 A coreful divisor d of n is a divisor that is divisible by every prime that divides n (see also A307958).
%C A372742 Numbers k such that A372739(k) = 1.
%C A372742 The corresponding values of m are in A372743.
%C A372742 Includes all prime numbers.
%H A372742 Amiram Eldar, <a href="/A372742/b372742.txt">Table of n, a(n) for n = 1..10000</a>
%F A372742 a(n) = A336563(A372743(n)).
%t A372742 f[p_, e_] := (p^(e + 1) - 1)/(p - 1) - 1; s[1] = 0; s[n_] := Times @@ f @@@ FactorInteger[n] - n; seq[max_] := Module[{v = Table[0, {max}], i}, Do[i = s[k]; If[1 <= i <= max, v[[i]]++], {k, 1, max^2}]; Position[v, 1] // Flatten]; seq[200]
%o A372742 (PARI) s(n) = {my(f = factor(n)); prod(i = 1, #f~, (f[i, 1]^(f[i, 2] + 1) - 1)/(f[i, 1] -1) - 1) - n;}
%o A372742 lista(nmax) = {my(v = vector(nmax), i); for(k=1, nmax^2, i = s(k); if(i > 0 && i <= nmax, v[i]++)); for(k = 1, nmax, if(v[k] == 1, print1(k, ", ")));}
%Y A372742 Cf. A336563, A372739, A372743.
%Y A372742 A000040 is a subsequence.
%Y A372742 Similar sequences: A057709, A357324, A361419.
%K A372742 nonn
%O A372742 1,1
%A A372742 _Amiram Eldar_, May 12 2024