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

Author

Antti Karttunen, Sep 26 2021

Keywords

• nonn

Examples

			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.
		

Links

• Index entries for sequences related to sigma(n)

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).

Programs

Mathematica

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

PARI

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