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A074848
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Number of 4-infinitary divisors of n: if n=Product p(i)^r(i) and d=Product p(i)^s(i), each s(i) has a digit a<=b in its 4-ary expansion everywhere that the corresponding r(i) has a digit b, then d is a 4-infinitary-divisor of n.
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1
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1, 2, 2, 3, 2, 4, 2, 4, 3, 4, 2, 6, 2, 4, 4, 2, 2, 6, 2, 6, 4, 4, 2, 8, 3, 4, 4, 6, 2, 8, 2, 4, 4, 4, 4, 9, 2, 4, 4, 8, 2, 8, 2, 6, 6, 4, 2, 4, 3, 6, 4, 6, 2, 8, 4, 8, 4, 4, 2, 12, 2, 4, 6, 6, 4, 8, 2, 6, 4, 8
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Multiplicative: If e = sum d_k 4^k, then a(p^e) = prod (d_k+1). Christian G. Bower (bowerc(AT)usa.net) May 19, 2005.
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EXAMPLE
| 2^4*3 is a 4-infinitary-divisor of 2^5*3^2 because 2^4*3 = 2^10*3^1 and 2^5*3^2 = 2^11*3^2 in 4-ary expanded power. All corresponding digits satisfy the condition. 1<=1, 0<=1, 1<=2.
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MAPLE
| A074848 := proc(n) if n= 1 then 1; else ifa := ifactors(n)[2] ; a := 1; for f in ifa do e := convert(op(2, f), base, 4) ; a := a*mul(d+1, d=e) ; end do: end if; end proc:
seq(A074848(n), n=1..70) ; # R. J. Mathar, Feb 08 2011
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CROSSREFS
| Cf. A038148.
Sequence in context: A084302 A080256 A035149 * A167447 A134687 A184395
Adjacent sequences: A074845 A074846 A074847 * A074849 A074850 A074851
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KEYWORD
| nonn,mult
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AUTHOR
| Yasutoshi Kohmoto (zbi74583(AT)boat.zero.ad.jp), Sep 10 2002
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