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 A306202 Matula-Goebel numbers of rooted semi-identity trees. 2
 1, 2, 3, 4, 5, 6, 7, 8, 10, 11, 12, 13, 14, 15, 16, 17, 19, 20, 21, 22, 24, 26, 28, 29, 30, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41, 42, 43, 44, 47, 48, 51, 52, 53, 55, 56, 57, 58, 59, 60, 62, 64, 65, 66, 67, 68, 70, 71, 73, 74, 76, 77, 78, 79, 80, 82, 84, 85 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Definition: A positive integer belongs to the sequence iff its prime indices greater than 1 are distinct and already belong to the sequence. A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798. LINKS EXAMPLE The sequence of all unlabeled rooted semi-identity trees together with their Matula-Goebel numbers begins:    1: o    2: (o)    3: ((o))    4: (oo)    5: (((o)))    6: (o(o))    7: ((oo))    8: (ooo)   10: (o((o)))   11: ((((o))))   12: (oo(o))   13: ((o(o)))   14: (o(oo))   15: ((o)((o)))   16: (oooo)   17: (((oo)))   19: ((ooo))   20: (oo((o)))   21: ((o)(oo))   22: (o(((o))))   24: (ooo(o))   26: (o(o(o)))   28: (oo(oo))   29: ((o((o))))   30: (o(o)((o))) MATHEMATICA primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]]; psidQ[n_]:=And[UnsameQ@@DeleteCases[primeMS[n], 1], And@@psidQ/@primeMS[n]]; Select[Range[100], psidQ] CROSSREFS Cf. A000081, A004111, A007097, A276625, A277098, A306200, A306201, A316467. Sequence in context: A122132 A325389 A020662 * A328335 A302569 A235034 Adjacent sequences:  A306199 A306200 A306201 * A306203 A306204 A306205 KEYWORD nonn AUTHOR Gus Wiseman, Jan 29 2019 STATUS approved

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Last modified January 26 17:16 EST 2020. Contains 331280 sequences. (Running on oeis4.)