A045765 n - d(n) never takes these values, where d(n) = A000005(n).

7, 8, 13, 19, 20, 24, 25, 28, 33, 36, 37, 40, 43, 49, 50, 52, 55, 56, 63, 64, 66, 67, 68, 74, 75, 79, 85, 88, 98, 100, 103, 108, 109, 112, 113, 116, 117, 123, 124, 126, 131, 132, 133, 134, 136, 140, 143, 145, 150, 153, 156, 159, 160, 163, 164, 167, 168

Offset

1,1

Comments

Complement of A236562. - Jaroslav Krizek, Feb 09 2014

Positions of zeros in A060990, leaf-nodes in the tree generated by edge-relation A049820(child) = parent. - Antti Karttunen, Oct 06 2015

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

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

Links

Antti Karttunen, Table of n, a(n) for n = 1..10000

Maple

N:= 1000: # to get all terms <= N
sort(convert({$1..N} minus {seq(x - numtheory:-tau(x), x=1..2*(1+N))}, list)); # Robert Israel, Oct 12 2015

Mathematica

lim = 10000; Take[Complement[Range@ lim, Sort@ DeleteDuplicates@ Table[n - DivisorSigma[0, n], {n, lim}]], 57] (* Michael De Vlieger, Oct 13 2015 *)

Prog

(PARI)
allocatemem((2^31)+(2^30));
uplim = 36756720 + 640; \\ = A002182(53) + A002183(53).
v060990 = vector(uplim);
for(n=3, uplim, v060990[n-numdiv(n)]++);
A060990 = n -> if(!n, 2, v060990[n]);
uplim2 = 36756720;
n=0; k=1; while(n <= uplim2, if(0==A060990(n), write("b045765_big.txt", k, " ", n); k++); n++; );
\\ Antti Karttunen, Oct 09 2015
(Scheme)
(define A045765 (ZERO-POS 1 1 A060990))
;; Using also IntSeq-library of Antti Karttunen, Oct 06 2015

Crossrefs

Top row of A262898.

Cf. A000005, A002183, A049820, A060990, A070319, A236562, A236565, A261100, A262511, A262686, A262901, A262902, A262903, A262909, A263081.

Cf. A263091 (primes in this sequence), A263095 (squares).

Cf. A259934 (gives the infinite trunk of the same tree, conjectured to be unique).

Sequence in context: A308833 A025156 A228210 * A118068 A060754 A196129

Adjacent sequences: A045762 A045763 A045764 * A045766 A045767 A045768

Keyword

nonn

Author

David W. Wilson

Status

approved