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A309306
Sums of two numbers such that neither of their number of divisors divides n but the number of divisors of their product and difference do.
0
30, 40, 80, 84, 126, 160, 180, 200, 210, 252, 270, 280, 288, 306, 320, 330, 360, 400, 420, 440, 450, 462, 468, 480, 520, 540, 546, 560, 576, 588, 594, 600, 612, 630, 640, 648, 660, 680, 704, 728, 756, 760, 780, 792, 800, 864, 880, 882, 900, 920, 924, 972
OFFSET
1,1
EXAMPLE
30 is in the sequence since 30 = 6 + 24; neither d(6) = 4 nor d(24) = 8 divide 30, but d(6*24) = d(144) = 15 | 30 and d(24-6) = d(18) = 6 | 30.
MATHEMATICA
Flatten[Table[If[Sum[(1 - Ceiling[n/DivisorSigma[0, i (n - i)]] + Floor[n/DivisorSigma[0, i (n - i)]]) (1 - Ceiling[n/DivisorSigma[0, n - 2 i]] + Floor[n/DivisorSigma[0, n - 2 i]]) (Ceiling[n/DivisorSigma[0, i]] - Floor[n/DivisorSigma[0, i]]) (Ceiling[n/DivisorSigma[0, n - i]] - Floor[n/DivisorSigma[0, n - i]]), {i, Floor[(n - 1)/2]}] > 0, n, {}], {n, 1000}]]
CROSSREFS
Cf. A033950.
Sequence in context: A025376 A280640 A152616 * A103250 A181638 A166650
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, Jul 21 2019
EXTENSIONS
Name corrected by Wesley Ivan Hurt, Jul 24 2019
STATUS
approved