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A306264
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a(n) = 1 + d*a(n/d); a(1)=0. If n has only one prime divisor, then d=n, otherwise d is the greatest proper unitary divisor of n.
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3
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0, 1, 1, 1, 1, 4, 1, 1, 1, 6, 1, 5, 1, 8, 6, 1, 1, 10, 1, 6, 8, 12, 1, 9, 1, 14, 1, 8, 1, 16, 1, 1, 12, 18, 8, 10, 1, 20, 14, 9, 1, 22, 1, 12, 10, 24, 1, 17, 1, 26, 18, 14, 1, 28, 12, 9, 20, 30, 1, 21, 1, 32, 10, 1, 14, 34, 1, 18, 24, 36, 1, 10, 1, 38, 26, 20, 12, 40, 1, 17
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OFFSET
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1,6
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COMMENTS
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Name related to recursive formula of A006022.
a(n) = 1 if and only if n is a prime power; p^t; t >= 1.
The sequence of indices k on which a(k) is a record (1,2,6,10,14,18,22,26,30,...), appears to be A111284.
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LINKS
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FORMULA
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EXAMPLE
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a(8) = a(25) = 1 because 8 and 25 are prime powers.
a(30) = 16 because 15 is the greatest proper unitary divisor of 30, so a(30) = 1 + 15*a(2) = 1 + 15 = 16.
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PROG
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(PARI) d(n) = if (omega(n) == 1, n, my(v=select(x->(gcd(x, n/x)==1), divisors(n))); v[#v-1]);
lista(nn) = {va = vector(nn); va[1] = 0; for (n=2, nn, dn = d(n); va[n] = 1 + dn*va[n/dn]; ); va; } \\ Michel Marcus, Feb 10 2019
(PARI)
A324388(n) = if(1>=omega(n), n, fordiv(n, d, if((d>1)&&(1==gcd(d, n/d)), return(n/d))));
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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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