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A327530
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Number of divisors of n that are 1 or whose prime indices are relatively prime.
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2
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1, 2, 1, 3, 1, 3, 1, 4, 1, 3, 1, 5, 1, 3, 2, 5, 1, 4, 1, 5, 1, 3, 1, 7, 1, 3, 1, 5, 1, 6, 1, 6, 2, 3, 2, 7, 1, 3, 1, 7, 1, 5, 1, 5, 3, 3, 1, 9, 1, 4, 2, 5, 1, 5, 2, 7, 1, 3, 1, 10, 1, 3, 1, 7, 1, 6, 1, 5, 2, 6, 1, 10, 1, 3, 3, 5, 2, 5, 1, 9, 1, 3, 1, 9, 2, 3
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OFFSET
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1,2
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COMMENTS
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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. Numbers whose prime indices are relatively prime are A289509. The maximum divisor of n that is 1 or whose prime indices are relatively prime is A327529(n).
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LINKS
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EXAMPLE
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The divisors of 84 that are 1 or whose prime indices are relatively prime are {1, 2, 4, 6, 12, 14, 28, 42, 84}, so a(84) = 9.
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MAPLE
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N:= 100: # for a(1)..a(N)
g:= proc(n) uses numtheory; igcd(op(map(pi, factorset(n))))=1 end proc:
V:= Vector(N, 1):
for k in select(g, [$2..N]) do
R:=[seq(i, i=k..N, k)]:
V[R]:= map(`+`, V[R], 1);
od:
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MATHEMATICA
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Table[Length[Select[Divisors[n], #==1||GCD@@PrimePi/@First/@FactorInteger[#]==1&]], {n, 100}]
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CROSSREFS
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See link for additional cross-references.
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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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