cp's OEIS Frontend

A386623 Numbers k such that k - A224787(k) is a square.

%I A386623 #13 Aug 01 2025 11:20:20
%S A386623 1,64,630,1225,1296,1750,1925,2079,3125,3402,3888,7150,11495,13000,
%T A386623 16445,16464,17160,17500,25578,25935,26082,27508,36975,39083,42688,
%U A386623 47125,55955,57188,61740,66671,85085,88451,99372,104544,111375,120736,122452,128898,137547,141427,145509,146927,152592
%N A386623 Numbers k such that k - A224787(k) is a square.
%C A386623 Numbers k such that k is the sum of a square and the cubes of the prime factors of k, counted with multiplicity.
%C A386623 Except for a(1) = 1, all terms are the product of at least 4 (not necessarily distinct) primes.
%C A386623 a(1) = 1 and a(7) = 1925 have k - A224787(k) = 1.  Are there any others? - _Will Gosnell_ and _Robert Israel_, Aug 01 2025
%H A386623 Robert Israel, <a href="/A386623/b386623.txt">Table of n, a(n) for n = 1..2511</a>
%e A386623 a(3) = 630 = 2 * 3^2 * 5 * 7 is a term because 630 - 2^3 - 2 * 3^3 - 5^3 - 7^3 = 100 is a square.
%p A386623 filter:= proc(n) local t;
%p A386623    issqr(n - add(t[1]^3*t[2],t=ifactors(n)[2]))
%p A386623 end proc:
%p A386623 select(filter, [$1..10^6]);
%Y A386623 Cf. A224787, A385238, A386245, A386304, A386640.
%K A386623 nonn
%O A386623 1,2
%A A386623 _Will Gosnell_ and _Robert Israel_, Jul 27 2025