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%I #32 Oct 16 2015 03:38:08
%S 7,8,13,19,20,24,25,28,33,36,37,40,43,49,50,52,55,56,63,64,66,67,68,
%T 74,75,79,85,88,98,100,103,108,109,112,113,116,117,123,124,126,131,
%U 132,133,134,136,140,143,145,150,153,156,159,160,163,164,167,168
%N n - d(n) never takes these values, where d(n) = A000005(n).
%C Complement of A236562. - _Jaroslav Krizek_, Feb 09 2014
%C Positions of zeros in A060990, leaf-nodes in the tree generated by edge-relation A049820(child) = parent. - _Antti Karttunen_, Oct 06 2015
%C Since A000005(x) <= 1 + x/2, n is in the sequence if there are no x <= 2*(n+1) with n = x - d(x). - _Robert Israel_, Oct 12 2015
%C This can be improved as: n is in the sequence if there are no x <= n + A002183(2+A261100(n)) with n = x - d(x). Cf. also A070319, A262686. - _Antti Karttunen_, Oct 12 2015
%H Antti Karttunen, <a href="/A045765/b045765.txt">Table of n, a(n) for n = 1..10000</a>
%p N:= 1000: # to get all terms <= N
%p sort(convert({$1..N} minus {seq(x - numtheory:-tau(x), x=1..2*(1+N))},list)); # _Robert Israel_, Oct 12 2015
%t lim = 10000; Take[Complement[Range@ lim, Sort@ DeleteDuplicates@ Table[n - DivisorSigma[0, n], {n, lim}]], 57] (* _Michael De Vlieger_, Oct 13 2015 *)
%o (PARI)
%o allocatemem((2^31)+(2^30));
%o uplim = 36756720 + 640; \\ = A002182(53) + A002183(53).
%o v060990 = vector(uplim);
%o for(n=3, uplim, v060990[n-numdiv(n)]++);
%o A060990 = n -> if(!n,2,v060990[n]);
%o uplim2 = 36756720;
%o n=0; k=1; while(n <= uplim2, if(0==A060990(n), write("b045765_big.txt", k, " ", n); k++); n++;);
%o \\ _Antti Karttunen_, Oct 09 2015
%o (Scheme)
%o (define A045765 (ZERO-POS 1 1 A060990))
%o ;; Using also IntSeq-library of _Antti Karttunen_, Oct 06 2015
%Y Top row of A262898.
%Y Cf. A000005, A002183, A049820, A060990, A070319, A236562, A236565, A261100, A262511, A262686, A262901, A262902, A262903, A262909, A263081.
%Y Cf. A263091 (primes in this sequence), A263095 (squares).
%Y Cf. A259934 (gives the infinite trunk of the same tree, conjectured to be unique).
%K nonn
%O 1,1
%A _David W. Wilson_
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