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A336423
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Number of strict chains of divisors from n to 1 using terms of A130091 (numbers with distinct prime multiplicities).
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20
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1, 1, 1, 2, 1, 0, 1, 4, 2, 0, 1, 5, 1, 0, 0, 8, 1, 5, 1, 5, 0, 0, 1, 14, 2, 0, 4, 5, 1, 0, 1, 16, 0, 0, 0, 0, 1, 0, 0, 14, 1, 0, 1, 5, 5, 0, 1, 36, 2, 5, 0, 5, 1, 14, 0, 14, 0, 0, 1, 0, 1, 0, 5, 32, 0, 0, 1, 5, 0, 0, 1, 35, 1, 0, 5, 5, 0, 0, 1, 36, 8, 0, 1, 0
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OFFSET
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1,4
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COMMENTS
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A number's prime signature (row n of A124010) is the sequence of positive exponents in its prime factorization, so a number has distinct prime multiplicities iff all the exponents in its prime signature are distinct.
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LINKS
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EXAMPLE
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The a(n) chains for n = 4, 8, 12, 16, 24, 32:
4/1 8/1 12/1 16/1 24/1 32/1
4/2/1 8/2/1 12/2/1 16/2/1 24/2/1 32/2/1
8/4/1 12/3/1 16/4/1 24/3/1 32/4/1
8/4/2/1 12/4/1 16/8/1 24/4/1 32/8/1
12/4/2/1 16/4/2/1 24/8/1 32/16/1
16/8/2/1 24/12/1 32/4/2/1
16/8/4/1 24/4/2/1 32/8/2/1
16/8/4/2/1 24/8/2/1 32/8/4/1
24/8/4/1 32/16/2/1
24/12/2/1 32/16/4/1
24/12/3/1 32/16/8/1
24/12/4/1 32/8/4/2/1
24/8/4/2/1 32/16/4/2/1
24/12/4/2/1 32/16/8/2/1
32/16/8/4/1
32/16/8/4/2/1
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MATHEMATICA
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strchns[n_]:=If[n==1, 1, If[!UnsameQ@@Last/@FactorInteger[n], 0, Sum[strchns[d], {d, Select[Most[Divisors[n]], UnsameQ@@Last/@FactorInteger[#]&]}]]];
Table[strchns[n], {n, 100}]
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CROSSREFS
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A336571 does not require n itself to have distinct prime multiplicities.
A007425 counts divisors of divisors.
A074206 counts strict chains of divisors from n to 1.
A130091 lists numbers with distinct prime multiplicities.
A181796 counts divisors with distinct prime multiplicities.
A253249 counts nonempty strict chains of divisors.
A327498 gives the maximum divisor with distinct prime multiplicities.
A337256 counts strict chains of divisors.
Cf. A001055, A002033, A005117, A032741, A067824, A071625, A118914, A124010, A167865, A336568, A336570, A336941.
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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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