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A263093 Numbers whose squares are in A045765.

%I A263093 #24 Mar 16 2025 02:38:42
%S A263093 5,6,7,8,10,14,16,18,20,22,26,27,28,34,35,37,46,47,50,54,56,58,59,60,
%T A263093 62,67,73,78,82,85,89,90,94,95,98,100,103,104,106,110,114,116,118,122,
%U A263093 124,125,126,127,128,130,135,140,141,142,148,150,155,158,161,164,170,172,174,177,178,182,184,188,190,199,202,205,207
%N A263093 Numbers whose squares are in A045765.
%C A263093 Numbers n such that there is no such k for which k - d(k) = n^2, where d(k) is the number of divisors of k (A000005).
%C A263093 Numbers n for which A060990(n^2) = A263087(n) = 0.
%H A263093 Antti Karttunen, <a href="/A263093/b263093.txt">Table of n, a(n) for n = 1..12443</a>
%H A263093 A. Karttunen, <a href="https://oeis.org/plot2a?name1=A263093&amp;name2=A263092&amp;tform1=untransformed&amp;tform2=untransformed&amp;shift=0&amp;radiop1=ratio&amp;drawlines=true">Ratio a(n)/A263092(n) drawn with the help of OEIS Plot2-utility</a>
%F A263093 a(n) = A000196(A263095(n)).
%o A263093 (PARI)
%o A263093 \\ Compute A263093 and A263095 at the same time:
%o A263093 A060990(n) = { my(k = n + 1440, s=0); while(k > n, if(((k-numdiv(k)) == n),s++); k--;); s}; \\ Hard limit 1440 is good for at least up to A002182(67) = 1102701600 as A002183(67) = 1440.
%o A263093 n = 1; k = 0; while((n^2)<1102701600, if((0 == A060990(n*n)), k++; write("b263093.txt", k, " ", n); write("b263095.txt", k, " ", (n*n)); ); n++; if(!(n%8192),print1(n,",k=", k, ", ")); );
%o A263093 (Scheme)
%o A263093 ;; With _Antti Karttunen_'s IntSeq-library.
%o A263093 (define A263093 (MATCHING-POS 1 1 (lambda (n) (zero? (A060990 (* n n))))))
%o A263093 (define A263093 (ZERO-POS 1 0 A263087))
%Y A263093 Cf. A000005, A000196, A045765, A049820, A060990, A263098.
%Y A263093 Complement: A263092.
%Y A263093 Positions of zeros in A263087 and positions of ones in A263088.
%Y A263093 Cf. A263095 (the squares of these numbers).
%K A263093 nonn
%O A263093 1,1
%A A263093 _Antti Karttunen_, Oct 11 2015