cp's OEIS Frontend

A263092 Numbers whose squares are in A236562; numbers n such that there is at least one such k for which k - d(k) = n^2, where d(k) is the number of divisors of k (A000005).

%I A263092 #22 Mar 16 2025 02:38:31
%S A263092 0,1,2,3,4,9,11,12,13,15,17,19,21,23,24,25,29,30,31,32,33,36,38,39,40,
%T A263092 41,42,43,44,45,48,49,51,52,53,55,57,61,63,64,65,66,68,69,70,71,72,74,
%U A263092 75,76,77,79,80,81,83,84,86,87,88,91,92,93,96,97,99,101,102,105,107,108,109
%N A263092 Numbers whose squares are in A236562; numbers n such that there is at least one such k for which k - d(k) = n^2, where d(k) is the number of divisors of k (A000005).
%C A263092 Starting offset is zero, because a(0)=0 is a special case in this sequence.
%C A263092 Numbers n for which A060990(n^2) = A263087(n) > 0.
%C A263092 Numbers n for which A049820(x) = n^2 has a solution.
%H A263092 Antti Karttunen, <a href="/A263092/b263092.txt">Table of n, a(n) for n = 0..20763</a>
%o A263092 (PARI)
%o A263092 \\ Compute A263092 and A263094 at the same time:
%o A263092 A060990(n) = { my(k = n + 1440, s=0); while(k > n, if(((k-numdiv(k)) == n),s++); k--;); s}; \\ Hard limit 1440 good for at least up to A002182(67) = 1102701600 as A002183(67) = 1440.
%o A263092 n = 0; k = 0; while((n^2)<1102701600, if((A060990(n*n) > 0), write("b263092.txt", k, " ", n); write("b263094.txt", k, " ", (n*n)); k++; ); n++; if(!(n%8192),print1(n,",k=", k, ", ")); );
%o A263092 (Scheme)
%o A263092 ;; With _Antti Karttunen_'s IntSeq-library.
%o A263092 (define A263092 (MATCHING-POS 0 0 (lambda (n) (not (zero? (A060990 (* n n)))))))
%o A263092 (define A263092 (NONZERO-POS 0 0 A263087))
%Y A263092 Complement: A263093.
%Y A263092 Cf. A000005, A000196, A049820, A060990, A236562, A263087, A263098.
%Y A263092 Cf. A263094 (the squares of these numbers).
%Y A263092 Cf. A262515 (a subsequence).
%K A263092 nonn
%O A263092 0,3
%A A263092 _Antti Karttunen_, Oct 11 2015