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 A325351 Heinz number of the augmented differences of the integer partition with Heinz number n. 21
 1, 2, 3, 4, 5, 6, 7, 8, 6, 10, 11, 12, 13, 14, 9, 16, 17, 12, 19, 20, 15, 22, 23, 24, 10, 26, 12, 28, 29, 18, 31, 32, 21, 34, 15, 24, 37, 38, 33, 40, 41, 30, 43, 44, 18, 46, 47, 48, 14, 20, 39, 52, 53, 24, 25, 56, 51, 58, 59, 36, 61, 62, 30, 64, 35, 42, 67, 68, 57, 30, 71, 48, 73, 74, 18, 76, 21, 66, 79, 80, 24, 82, 83, 60, 55, 86, 69, 88, 89, 36, 35 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k). The augmented differences aug(y) of an integer partition y of length k are given by aug(y)_i = y_i - y_{i + 1} + 1 if i < k and aug(y)_k = y_k. For example, aug(6,5,5,3,3,3) = (2,1,3,1,1,3). Note that aug preserves length so this sequence preserves omega (number of prime factors counted with multiplicity). LINKS Antti Karttunen, Table of n, a(n) for n = 1..16384 EXAMPLE The partition (3,2,2,1) with Heinz number 90 has augmented differences (2,1,2,1) with Heinz number 36, so a(90) = 36. MATHEMATICA primeptn[n_]:=If[n==1, {}, Reverse[Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]]]; aug[y_]:=Table[If[i1, f[i, 2]--, i--)); if(pi, listput(diffs, pi)); Vec(diffs); }; A325351(n) = factorback(apply(prime, augdiffs(n))); \\ Antti Karttunen, Nov 16 2019 CROSSREFS Number of appearances of n is A008480(n). Cf. A056239, A093641 (fixed points), A112798, A325350, A325352, A325355, A325366, A325389, A325394, A325395, A325396. Sequence in context: A063917 A234344 A331298 * A279319 A171890 A287793 Adjacent sequences:  A325348 A325349 A325350 * A325352 A325353 A325354 KEYWORD nonn,look AUTHOR Gus Wiseman, Apr 23 2019 EXTENSIONS More terms from Antti Karttunen, Nov 16 2019 STATUS approved

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Last modified January 19 21:47 EST 2020. Contains 331066 sequences. (Running on oeis4.)