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A348034
Numbers k that have at least one unitary divisor d such that sigma(d)*d is equal to k.
2
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
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
KEYWORD
nonn
AUTHOR
Antti Karttunen, Sep 26 2021
STATUS
approved