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A281668
Expansion of Sum_{p prime, i>=1} x^(p^i)/(1 + x^(p^i)) * Product_{p prime, j>=1} (1 + x^(p^j)).
1
0, 1, 1, 1, 3, 2, 5, 3, 8, 7, 10, 12, 13, 20, 18, 26, 25, 36, 34, 45, 47, 59, 62, 71, 82, 91, 105, 112, 132, 143, 163, 174, 201, 220, 244, 266, 298, 327, 362, 388, 437, 470, 521, 558, 621, 671, 733, 788, 864, 938, 1011, 1100, 1182, 1295, 1379, 1501, 1606, 1753, 1861, 2017, 2158, 2335, 2493, 2672, 2871, 3078
OFFSET
1,5
COMMENTS
Total number of parts in all partitions of n into distinct prime power parts (1 excluded).
FORMULA
G.f.: Sum_{p prime, i>=1} x^(p^i)/(1 + x^(p^i)) * Product_{p prime, j>=1} (1 + x^(p^j)).
EXAMPLE
a(10) = 7 because we have [8, 2], [7, 3], [5, 3, 2] and 2 + 2 + 3 = 7.
MATHEMATICA
nmax = 66; Rest[CoefficientList[Series[Sum[Floor[1/PrimeNu[i]] x^i/(1 + x^i), {i, 2, nmax}] Product[1 + Floor[1/PrimeNu[j]] x^j, {j, 2, nmax}], {x, 0, nmax}], x]]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Jan 26 2017
STATUS
approved