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A341309
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Sum of odd divisors of n that are <= A003056(n).
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5
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1, 1, 1, 1, 1, 4, 1, 1, 4, 1, 1, 4, 1, 1, 9, 1, 1, 4, 1, 6, 4, 1, 1, 4, 6, 1, 4, 8, 1, 9, 1, 1, 4, 1, 13, 4, 1, 1, 4, 6, 1, 11, 1, 1, 18, 1, 1, 4, 8, 6, 4, 1, 1, 13, 6, 8, 4, 1, 1, 9, 1, 1, 20, 1, 6, 15, 1, 1, 4, 13, 1, 13, 1, 1, 9, 1, 19, 4, 1, 6, 13, 1, 1, 11, 6, 1, 4, 12, 1, 18, 21
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OFFSET
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1,6
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COMMENTS
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Conjecture 1: a(n) is also the total number de parts in all partitions of n into an odd number of consecutive parts. - Omar E. Pol, Mar 16 2022
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LINKS
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FORMULA
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MATHEMATICA
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A341309[n_]:=With[{t=Floor[(Sqrt[8n+1]-1)/2]}, DivisorSum[n, #&, OddQ[#]&&#<=t&]];
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PROG
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(PARI) a(n) = my(m=n>>valuation(n, 2), s=(sqrtint(8*n+1)-1)\2); sumdiv(m, d, if (d <= s, d)); \\ Michel Marcus, Mar 25 2023
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CROSSREFS
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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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