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A220483
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Total number of smallest parts that are also emergent parts in all partitions of n with at least one distinct part: a(n) = n + d(n) + p(n-1) + spt(n) - A000070(n) - sigma(n) - 1.
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1
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0, 0, 0, 0, 0, 0, 1, 1, 3, 5, 8, 11, 19, 26, 34, 51, 67, 91, 118, 158, 200, 271, 331, 433, 538, 699, 849, 1089, 1323, 1674, 2030, 2542, 3066, 3813, 4567, 5640, 6760, 8272, 9871, 12002, 14290, 17287, 20515, 24675, 29214, 34981, 41282, 49216, 57957, 68798
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OFFSET
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1,9
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COMMENTS
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LINKS
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FORMULA
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MATHEMATICA
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b[n_, i_] := b[n, i] = If[n==0 || i==1, n, {q, r} = QuotientRemainder[n, i]; If[r == 0, q, 0] + Sum[b[n - i*j, i - 1], {j, 0, n/i}]];
a[n_] := n + DivisorSigma[0, n] + PartitionsP[n - 1] + b[n, n] -
Total[PartitionsP[Range[0, n]]] - DivisorSigma[1, n] - 1;
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CROSSREFS
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Cf. A000005, A000041, A000070, A000203, A002865, A092269, A182699, A182709, A183152, A193827, A195820, A206437, A215513, A220479, A220489.
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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