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Numbers n for which there is exactly one solution to x - d(x) = n, where d(n) is the number of divisors of n (A000005). Positions of ones in A060990.
12

%I #14 Oct 02 2015 12:13:46

%S 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 59,60,61,71,72,73,76,77,80,82,83,84,86,89,90,92,93,94,95,97,99,101,

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

%H Antti Karttunen, <a href="/A262511/b262511.txt">Table of n, a(n) for n = 1..100000</a>

%F Other identities. For all n >= 1:

%F a(n) = A049820(A262512(n)).

%o (PARI)

%o allocatemem(123456789);

%o uplim = 14414400 + 504; \\ = A002182(49) + A002183(49).

%o v060990 = vector(uplim);

%o for(n=3, uplim, v060990[n-numdiv(n)]++);

%o A060990 = n -> if(!n,2,v060990[n]);

%o uplim2 = 14414400;

%o n=0; k=1; while(n <= uplim2, if(1==A060990(n), write("b262511_big.txt", k, " ", n); k++); n++;);

%o (Scheme, with _Antti Karttunen_'s IntSeq-library)

%o (define A262511 (ZERO-POS 1 1 (COMPOSE -1+ A060990)))

%Y Cf. A000005, A049820, A060990.

%Y Cf. A262512 (gives the corresponding x).

%Y Cf. A262510 (a subsequence).

%Y Subsequence of A236562.

%K nonn

%O 1,1

%A _Antti Karttunen_, Sep 25 2015