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A320230
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Matula-Goebel numbers of rooted trees in which the non-leaf branches directly under any given node are all equal.
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11
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1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 16, 17, 18, 19, 20, 22, 23, 24, 25, 26, 27, 28, 29, 31, 32, 34, 36, 37, 38, 40, 41, 43, 44, 46, 48, 49, 50, 52, 53, 54, 56, 58, 59, 61, 62, 64, 67, 68, 71, 72, 74, 76, 79, 80, 81, 82, 83, 86, 88, 89, 92, 96, 97
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OFFSET
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1,2
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COMMENTS
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A number is in the sequence iff it belongs to A070776 and its prime indices already belong to the sequence. A prime index of n is a number m such that prime(m) divides n.
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LINKS
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MATHEMATICA
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primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]]
smakQ[n_]:=And[SameQ@@DeleteCases[primeMS[n], 1], And@@smakQ/@DeleteCases[primeMS[n], 1]]; Select[Range[100], smakQ[#]&]
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PROG
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(PARI) is(n) = while((n>>=valuation(n, 2)) > 1, isprimepower(n, &n) || return(0); n=primepi(n)); 1; \\ Kevin Ryde, Apr 04 2021
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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