A045765 - OEIS

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

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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);