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 A305732 Heinz numbers of reducible integer partitions. Numbers n > 1 that are prime or whose prime indices are relatively prime and such that A181819(n) is already in the sequence. 11
 2, 3, 4, 5, 6, 7, 8, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 22, 23, 24, 26, 28, 29, 30, 31, 32, 33, 34, 35, 37, 38, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 53, 54, 55, 56, 58, 59, 60, 61, 62, 64, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k). A prime index of n is a number m such that prime(m) divides n. A multiset m whose distinct elements are m_1, m_2, ..., m_k with multiplicities y_1, y_2, ..., y_k is reducible if either m is of size 1 or gcd(m_1,...,m_k) = 1 and the multiset {y_1,...,y_k} is also reducible. LINKS EXAMPLE 60 has relatively prime prime indices {1,1,2,3} with multiplicities {1,1,2} corresponding to A181819(90) = 12. 12 has relatively prime prime indices {1,1,2} with multiplicities {1,2} corresponding to A181819(12) = 6. 6 has relatively prime prime indices {1,2} with multiplicities {1,1} corresponding to A181819(6) = 4. 4 has relatively prime prime indices {1,1} with multiplicities {2} corresponding to A181819(4) = 3. 3 is prime, so we conclude that 60 belongs to the sequence. MATHEMATICA rdzQ[n_]:=And[n>1, Or[PrimeQ[n], And[rdzQ[Times@@Prime/@FactorInteger[n][[All, 2]]], GCD@@PrimePi/@FactorInteger[n][[All, 1]]==1]]]; Select[Range[50], rdzQ] CROSSREFS Cf. A000837, A007916, A056239, A181819, A182850, A289508, A289509, A298748, A304465, A304687, A304818, A305563, A305731, A305733. Sequence in context: A317492 A324721 A327534 * A265999 A316502 A316495 Adjacent sequences:  A305729 A305730 A305731 * A305733 A305734 A305735 KEYWORD nonn AUTHOR Gus Wiseman, Jun 22 2018 STATUS approved

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Last modified April 17 09:29 EDT 2021. Contains 343064 sequences. (Running on oeis4.)