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A319272 Numbers whose prime multiplicities are distinct and whose prime indices are term of the sequence. 1
1, 2, 3, 4, 5, 7, 8, 9, 11, 12, 16, 17, 18, 19, 20, 23, 24, 25, 27, 28, 31, 32, 37, 40, 44, 45, 48, 49, 50, 53, 54, 56, 59, 61, 63, 64, 67, 68, 71, 72, 75, 76, 80, 81, 83, 88, 89, 92, 96, 97, 98, 99, 103, 107, 108, 112, 121, 124, 125, 127, 128, 131, 135, 136, 144, 147, 148 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
A prime index of n is a number m such that prime(m) divides n.
Also Matula-Goebel numbers of rooted trees in which the multiplicities in the multiset of branches directly under any given node are distinct.
LINKS
EXAMPLE
36 is not in the sequence because 36 = 2^2 * 3^2 does not have distinct prime multiplicities.
The sequence of terms of the sequence followed by their Matula-Goebel trees begins:
1: o
2: (o)
3: ((o))
4: (oo)
5: (((o)))
7: ((oo))
8: (ooo)
9: ((o)(o))
11: ((((o))))
12: (oo(o))
16: (oooo)
17: (((oo)))
18: (o(o)(o))
19: ((ooo))
20: (oo((o)))
23: (((o)(o)))
24: (ooo(o))
25: (((o))((o)))
27: ((o)(o)(o))
28: (oo(oo))
31: (((((o)))))
MATHEMATICA
mgsiQ[n_]:=Or[n==1, And[UnsameQ@@Last/@FactorInteger[n], And@@Cases[FactorInteger[n], {p_, _}:>mgsiQ[PrimePi[p]]]]];
Select[Range[100], mgsiQ]
PROG
(PARI) is(n)={my(f=factor(n)); if(#Set(f[, 2])<#f~, 0, for(i=1, #f~, if(!is(primepi(f[i, 1])), return(0))); 1)}
{ select(is, [1..200]) } \\ Andrew Howroyd, Mar 01 2020
CROSSREFS
Sequence in context: A288221 A346782 A229757 * A366142 A141819 A097904
KEYWORD
nonn
AUTHOR
Gus Wiseman, Sep 16 2018
EXTENSIONS
Terms a(53) and beyond from Andrew Howroyd, Mar 01 2020
STATUS
approved

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Last modified March 28 17:42 EDT 2024. Contains 371254 sequences. (Running on oeis4.)