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A324121
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a(n) = gcd(n*d(n), sigma(n)), where d(n) = number of divisors of n (A000005) and sigma(n) = sum of divisors of n (A000203).
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10
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1, 1, 2, 1, 2, 12, 2, 1, 1, 2, 2, 4, 2, 8, 12, 1, 2, 3, 2, 6, 4, 4, 2, 12, 1, 2, 4, 56, 2, 24, 2, 3, 12, 2, 4, 1, 2, 4, 4, 10, 2, 48, 2, 12, 6, 8, 2, 4, 3, 3, 12, 2, 2, 24, 4, 8, 4, 2, 2, 24, 2, 8, 2, 1, 4, 48, 2, 6, 12, 16, 2, 3, 2, 2, 2, 4, 4, 24, 2, 2, 1, 2, 2, 112, 4, 4, 12, 4, 2, 18, 28, 24, 4, 8, 20, 36, 2, 3, 6, 1, 2, 24, 2, 2, 24
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OFFSET
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1,3
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COMMENTS
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Records 1, 2, 12, 56, 112, 120, 336, 720, 992, 2016, 4368, 8640, 14880, 16256, 26208, 59520, 78624, 120960, 131040, 191520, 227584, 297600, ... occur at positions: 1, 3, 6, 28, 84, 120, 140, 270, 496, 672, 1638, 2970, 6200, 8128, 8190, 18600, 27846, 30240, 32760, 55860, 105664, 117800, ... . Note that A001599 is not a subsequence of the latter, as at least 18620 (present in A001599) is missing.
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LINKS
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FORMULA
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MATHEMATICA
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Table[GCD[n DivisorSigma[0, n], DivisorSigma[1, n]], {n, 120}] (* Harvey P. Dale, Feb 17 2023 *)
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PROG
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(PARI) A324121(n) = gcd(sigma(n), n*numdiv(n));
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CROSSREFS
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Cf. A000005, A000203, A001599, A038040, A106315, A106316, A156552, A324045, A324046, A324047, A324058, A324122.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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