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 A240205 Number of partitions p of n such that mean(p) = multiplicity(min(p)). 5
 0, 1, 0, 0, 1, 0, 1, 0, 2, 1, 2, 0, 4, 0, 2, 7, 3, 0, 17, 0, 5, 26, 2, 0, 60, 1, 2, 61, 59, 0, 91, 0, 149, 119, 2, 34, 480, 0, 2, 215, 788, 0, 288, 0, 1147, 923, 2, 0, 2528, 1, 1585, 611, 3319, 0, 1150, 3963, 5366, 986, 2, 0, 20317 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,9 COMMENTS a(n) = 0 if and only if n = 0 or n is a prime. LINKS FORMULA a(n) = A240204(n) - A240203(n) for n >= 0. a(n) + A240203(n) + A240206(n) = A000041(n) for n >= 0. EXAMPLE a(12) counts these 4 partitions:  9111, 6222, 422211, 332211. MATHEMATICA z = 60; f[n_] := f[n] = IntegerPartitions[n]; t1 = Table[Count[f[n], p_ /; Mean[p] < Count[p, Min[p]]], {n, 0, z}]  (* A240203 *) t2 = Table[Count[f[n], p_ /; Mean[p] <= Count[p, Min[p]]], {n, 0, z}] (* A240204 *) t3 = Table[Count[f[n], p_ /; Mean[p] == Count[p, Min[p]]], {n, 0, z}] (* A240205 *) t4 = Table[Count[f[n], p_ /; Mean[p] > Count[p, Min[p]]], {n, 0, z}] (* A240206 *) t5 = Table[Count[f[n], p_ /; Mean[p] >= Count[p, Min[p]]], {n, 0, z}] (* A240079 *) CROSSREFS Cf. A240203, A240204, A240206, A240079, A000041. Sequence in context: A138498 A276669 A307596 * A050319 A132456 A257873 Adjacent sequences:  A240202 A240203 A240204 * A240206 A240207 A240208 KEYWORD nonn,easy AUTHOR Clark Kimberling, Apr 03 2014 STATUS approved

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Last modified July 19 03:54 EDT 2019. Contains 325144 sequences. (Running on oeis4.)