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 A074848 Number of 4-infinitary divisors of n. 7
 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, 2, 12, 2, 4, 6, 6, 4, 8, 2, 4, 2, 4, 2, 12, 4, 4, 4, 8, 2, 12, 4, 6, 4, 4, 4, 8, 2, 6, 6, 9, 2, 8, 2, 8, 8 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS 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. LINKS Antti Karttunen, Table of n, a(n) for n = 1..10000 FORMULA Multiplicative: If e = sum d_k 4^k, then a(p^e) = prod (d_k+1). - Christian G. Bower, May 19 2005 a(1) = 1; for n > 1, a(n) = A268444(A067029(n)) * a(A028234(n)). [After _Christian G. Bower's 2005 formula.] - Antti Karttunen, May 28 2017 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. 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 MATHEMATICA f[p_, e_] := Times @@ (IntegerDigits[e, 4] + 1); a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100]  (* Amiram Eldar, Sep 09 2020 *) PROG (PARI) A268444(n) = { my(m=1, d); while(n, d = (n%4); m *= (1+d); n = (n-d)/4); m; }; A074848(n) = factorback(apply(e -> A268444(e), factorint(n)[, 2])) \\ (After A037445) - Antti Karttunen, May 28 2017 (Scheme) (definec (A074848 n) (if (= 1 n) n (* (A268444 (A067029 n)) (A074848 (A028234 n))))) ;; Antti Karttunen, May 28 2017 CROSSREFS Cf. A037445, A038148, A074847, A268444. Sequence in context: A299701 A286605 A035149 * A252505 A325560 A318412 Adjacent sequences:  A074845 A074846 A074847 * A074849 A074850 A074851 KEYWORD nonn,mult AUTHOR Yasutoshi Kohmoto, Sep 10 2002 EXTENSIONS More terms from Antti Karttunen, May 28 2017 Name shortened by Amiram Eldar, Sep 09 2020 STATUS approved

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Last modified November 29 18:41 EST 2021. Contains 349416 sequences. (Running on oeis4.)