A348034 Numbers k that have at least one unitary divisor d such that sigma(d)*d is equal to k.

1, 6, 12, 28, 30, 56, 117, 120, 132, 182, 306, 380, 496, 552, 672, 775, 870, 992, 1080, 1406, 1680, 1722, 1892, 2016, 2184, 2256, 2793, 2862, 3276, 3540, 3782, 3960, 4556, 4560, 4650, 5112, 5402, 5460, 6320, 6552, 6972, 7392, 8010, 8128, 9180, 9300, 9506, 9801, 10302, 10712, 11556, 11904, 11990, 12882, 16093, 16256

Offset

1,2

Links

Table of n, a(n) for n=1..56.

Index entries for sequences related to sigma(n)

Example

120 = 2^3 * 3 * 5 has a unitary divisor 8 for which sigma(8) = 15 = 120/8, thus 120 is included in the sequence.
672 = 2^5 * 3 * 7 has a unitary divisor 21 for which sigma(21) = 32 = 120/21, thus 672 is included in the sequence.

Mathematica

q[n_] := DivisorSum[n, 1 &, CoprimeQ[#, n/#] && #*DivisorSigma[1, #] == n &] > 0; Select[Range[16256], q] (* Amiram Eldar, Sep 27 2021 *)

Prog

(PARI) isA348034(n) = { fordiv(n, d, if(1==gcd(d, n/d)&&n==d*sigma(d), return(1))); (0); };

Crossrefs

Subsequence of A327165. Even terms of A000396 are all present.

Positions of nonzero terms in A348033.

Cf. also A348035 (multiply-perfect numbers in this sequence).

Sequence in context: A327165 A338520 A339472 * A086792 A064987 A057341

Adjacent sequences: A348031 A348032 A348033 * A348035 A348036 A348037

Keyword

nonn

Author

Antti Karttunen, Sep 26 2021

Status

approved