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A145388
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a(n)= sum of (k,n)_* for k=1,2,...,n, where (k,n)_* is the greatest divisor of k which is a unitary divisor of n
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1
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1, 3, 5, 7, 9, 15, 13, 15, 17, 27, 21, 35, 25, 39, 45, 31, 33, 51, 37, 63, 65, 63, 45, 75, 49, 75, 53, 91, 57, 135, 61, 63, 105, 99, 117, 119, 73, 111, 125, 135, 81, 195, 85, 147, 153, 135, 93, 155, 97, 147, 165, 175, 105, 159
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| A unitary analogue of Pillai's function A018804; another unitary analogue of A018804 is A089912.
The sequence is the row sums of the following triangle of (k,n)_* with rows n and columns 1<=k<=n (R. J. Mathar, Jun 01 2011):
1
1 2
1 1 3
1 1 1 4
1 1 1 1 5
1 2 3 2 1 6
1 1 1 1 1 1 7
1 1 1 1 1 1 1 8
1 1 1 1 1 1 1 1 9
1 2 1 2 5 2 1 2 1 10
1 1 1 1 1 1 1 1 1 1 11
1 1 3 4 1 3 1 4 3 1 1 12
1 1 1 1 1 1 1 1 1 1 1 1 13
1 2 1 2 1 2 7 2 1 2 1 2 1 14
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REFERENCES
| L. Toth, The unitary analogue of Pillai's arithmetical function, Collect. Math., 40 (1989), 19-30.
L. Toth, The unitary analogue of Pillai's arithmetical function II., Notes Number Theory Discrete Math., 2 (1996), no 2, 40-46.
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FORMULA
| Multiplicative: a(p^e)=2*p^e-1 for every prime power p^e
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MAPLE
| A145388 := proc(n) option remember; local pf, p ; if n = 1 then 1; else pf := ifactors(n)[2] ; if nops(pf) = 1 then 2*n-1 ; else mul(procname(op(1, p)^op(2, p)), p=pf) ; end if; end if; end proc:
seq(A145388(n), n=1..70) ; # R. J. Mathar, Jan 07 2011
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CROSSREFS
| Sequence in context: A107220 A098758 A029608 * A121820 A180204 A006995
Adjacent sequences: A145385 A145386 A145387 * A145389 A145390 A145391
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KEYWORD
| mult,nonn
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AUTHOR
| Laszlo Toth (ltoth(AT)ttk.pte.hu), Oct 10 2008
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