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A320230
Matula-Goebel numbers of rooted trees in which the non-leaf branches directly under any given node are all equal.
11
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
OFFSET
1,2
COMMENTS
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.
MATHEMATICA
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[#]&]
PROG
(PARI) is(n) = while((n>>=valuation(n, 2)) > 1, isprimepower(n, &n) || return(0); n=primepi(n)); 1; \\ Kevin Ryde, Apr 04 2021
KEYWORD
nonn
AUTHOR
Gus Wiseman, Oct 08 2018
STATUS
approved