A348033 Number of unitary divisors d of n such that sigma(d)*d is equal to n.

1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1

Offset

1

Comments

Differs from A327153 for the first time at n=72, where a(72)=0, while A327153(72) = 1.

Conjecture: For all terms x > 1 of A019278, a(x) = 0.

Question: Are there any terms larger than 1?

Links

Table of n, a(n) for n=1..120.

Index entries for sequences related to sigma(n)

Formula

a(n) = Sum_{d|n} [1==gcd(d, n/d) and A000203(d)*d == n], where [ ] is the Iverson bracket.

For all n, a(n) <= A327153(n).

Mathematica

a[n_] := DivisorSum[n, 1 &, CoprimeQ[#, n/#] && #*DivisorSigma[1, #] == n &]; Array[a, 120] (* Amiram Eldar, Sep 27 2021 *)

Prog

(PARI) A348033(n) = sumdiv(n, d, if(1==gcd(d, n/d)&&n==(d*sigma(d)), 1, 0));

Crossrefs

Cf. A019278, A327153, A348034 (positions of nonzero terms), A348035.

Sequence in context: A205809 A353370 A355940 * A327153 A133943 A014084

Adjacent sequences: A348030 A348031 A348032 * A348034 A348035 A348036

Keyword

nonn

Author

Antti Karttunen, Sep 26 2021

Status

approved