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Search: id:A055210
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| A055210 |
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Sum of totients of square divisors of n. |
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+0
2
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| 1, 1, 1, 3, 1, 1, 1, 3, 7, 1, 1, 3, 1, 1, 1, 11, 1, 7, 1, 3, 1, 1, 1, 3, 21, 1, 7, 3, 1, 1, 1, 11, 1, 1, 1, 21, 1, 1, 1, 3, 1, 1, 1, 3, 7, 1, 1, 11, 43, 21, 1, 3, 1, 7, 1, 3, 1, 1, 1, 3, 1, 1, 7, 43, 1, 1, 1, 3, 1, 1, 1, 21, 1, 1, 21, 3, 1, 1, 1, 11, 61, 1, 1, 3, 1, 1, 1, 3, 1, 7, 1, 3, 1, 1, 1, 11, 1
(list; graph; listen)
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OFFSET
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1,4
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FORMULA
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a(n) = Sum[Phi[d]; d is square and divides n]
Multiplicative with a(p^e) = (p^(e+1)+1)/(p+1) for even e and a(p^e) = (p^e+1)/(p+1) for odd e. - Vladeta Jovovic (vladeta(AT)eunet.rs), Dec 01 2001
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EXAMPLE
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n = 400: its square divisors are {1, 4, 16, 25, 100, 400}, their totients are {1, 2, 8, 20, 40, 160} and the totient-sum over these divisors is, so a(400) = 231. This value arises at special square-free multiples of 400 (400 times 2, 3, 5, 6, 7, 10, 11, 13, 15, 17, 19, 21, 22, 23 etc.)
a(400) = a(2^4*5^2) = (2^5+1)/3*(5^3+1)/6 = 231.
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CROSSREFS
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Sequence in context: A131270 A109223 A016466 this_sequence A082553 A143632 A130605
Adjacent sequences: A055207 A055208 A055209 this_sequence A055211 A055212 A055213
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KEYWORD
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nonn,mult
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AUTHOR
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Labos E. (labos(AT)ana.sote.hu), Jun 19 2000
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