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A262511 Numbers k for which there is exactly one solution to x - d(x) = k, where d(k) is the number of divisors of k (A000005). Positions of ones in A060990.

%I A262511 #21 Jun 19 2025 11:12:02
%S A262511 2,3,4,5,9,10,12,14,15,16,18,21,23,26,30,31,32,41,42,44,45,47,53,54,
%T A262511 59,60,61,71,72,73,76,77,80,82,83,84,86,89,90,92,93,94,95,97,99,101,
%U A262511 104,105,106,110,115,119,121,122,127,135,139,146,148,149,151,154,158,161,169,171,173,176,177,183,186,188,189,190,191,192,194,195,199,200,202
%N A262511 Numbers k for which there is exactly one solution to x - d(x) = k, where d(k) is the number of divisors of k (A000005). Positions of ones in A060990.
%H A262511 Antti Karttunen, <a href="/A262511/b262511.txt">Table of n, a(n) for n = 1..100000</a>
%F A262511 Other identities. For all n >= 1:
%F A262511 a(n) = A049820(A262512(n)).
%o A262511 (PARI)
%o A262511 allocatemem(123456789);
%o A262511 uplim = 14414400 + 504; \\ = A002182(49) + A002183(49).
%o A262511 v060990 = vector(uplim);
%o A262511 for(n=3, uplim, v060990[n-numdiv(n)]++);
%o A262511 A060990 = n -> if(!n,2,v060990[n]);
%o A262511 uplim2 = 14414400;
%o A262511 n=0; k=1; while(n <= uplim2, if(1==A060990(n), write("b262511_big.txt", k, " ", n); k++); n++;);
%o A262511 (Scheme)
%o A262511 ;; With _Antti Karttunen_'s IntSeq-library.
%o A262511 (define A262511 (ZERO-POS 1 1 (COMPOSE -1+ A060990)))
%Y A262511 Cf. A000005, A049820, A060990.
%Y A262511 Cf. A262512 (gives the corresponding x).
%Y A262511 Cf. A262510 (a subsequence).
%Y A262511 Subsequence of A236562.
%K A262511 nonn
%O A262511 1,1
%A A262511 _Antti Karttunen_, Sep 25 2015