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A327163
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Lexicographically earliest sequence such that for all i, j, a(i) = a(j) => f(i) = f(j), where f(n) = gcd(n,usigma(n)) * (-1)^[gcd(n,usigma(n))==n], and usigma is the sum of unitary divisors of n (A034448).
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2
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1, 2, 2, 2, 2, 3, 2, 2, 2, 4, 2, 5, 2, 4, 6, 2, 2, 7, 2, 8, 2, 4, 2, 9, 2, 4, 2, 5, 2, 7, 2, 2, 6, 4, 2, 4, 2, 4, 2, 4, 2, 7, 2, 5, 10, 4, 2, 5, 2, 4, 6, 4, 2, 7, 2, 11, 2, 4, 2, 12, 2, 4, 2, 2, 2, 7, 2, 4, 6, 4, 2, 13, 2, 4, 2, 5, 2, 7, 2, 4, 2, 4, 2, 5, 2, 4, 6, 5, 2, 14, 15, 5, 2, 4, 16, 9, 2, 4, 6, 8, 2, 7, 2, 4, 6
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OFFSET
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1,2
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COMMENTS
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Restricted growth sequence transform of function f, defined as f(n) = -A323166(n) = -n when n is one of unitary multiply-perfect numbers (A327158), otherwise f(n) = A323166(n) = gcd(n,A034448(n))
For all i, j:
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LINKS
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PROG
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(PARI)
up_to = 87360;
rgs_transform(invec) = { my(om = Map(), outvec = vector(length(invec)), u=1); for(i=1, length(invec), if(mapisdefined(om, invec[i]), my(pp = mapget(om, invec[i])); outvec[i] = outvec[pp] , mapput(om, invec[i], i); outvec[i] = u; u++ )); outvec; };
A034448(n) = { my(f=factorint(n)); prod(k=1, #f~, 1+(f[k, 1]^f[k, 2])); }; \\ After code in A034448
Aux327163(n) = { my(u=A323166(n)); u*((-1)^(u==n)); };
v327163 = rgs_transform(vector(up_to, n, Aux327163(n)));
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CROSSREFS
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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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