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A318307 Multiplicative with a(p^e) = 2^A002487(e). 6
1, 2, 2, 2, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 4, 2, 2, 4, 2, 4, 4, 4, 2, 8, 2, 4, 4, 4, 2, 8, 2, 8, 4, 4, 4, 4, 2, 4, 4, 8, 2, 8, 2, 4, 4, 4, 2, 4, 2, 4, 4, 4, 2, 8, 4, 8, 4, 4, 2, 8, 2, 4, 4, 4, 4, 8, 2, 4, 4, 8, 2, 8, 2, 4, 4, 4, 4, 8, 2, 4, 2, 4, 2, 8, 4, 4, 4, 8, 2, 8, 4, 4, 4, 4, 4, 16, 2, 4, 4, 4, 2, 8, 2, 8, 8 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..16384

Index entries for sequences computed from exponents in factorization of n

FORMULA

a(n) = 2^A318306(n).

a(n) = A061142(A318470(n)).

a(n^2) = a(n).

a(A003557(n^2)) = A318316(n).

Dirichlet convolution square of A318667(n)/A317934(n).

MATHEMATICA

f[m_] := Module[{a = 1, b = 0, n = m}, While[n > 0, If[OddQ[n], b += a, a += b]; n = Floor[n/2]]; b]; Array[Times @@ Map[2^f@ # &, FactorInteger[#][[All, -1]] ] - Boole[# == 1] &, 105] (* after Jean-Fran├žois Alcover at A002487 *)

PROG

(PARI)

A002487(n) = { my(a=1, b=0); while(n>0, if(bitand(n, 1), b+=a, a+=b); n>>=1); (b); }; \\ From A002487

A318307(n) = factorback(apply(e -> 2^A002487(e), factor(n)[, 2]));

CROSSREFS

Cf. A318306, A318316, A318470, A318667.

Differs from A037445 for the first time at n=32, where a(32) = 8, while A037445(32) = 4.

Sequence in context: A154851 A281854 A037445 * A286324 A318472 A186643

Adjacent sequences:  A318304 A318305 A318306 * A318308 A318309 A318310

KEYWORD

nonn,mult

AUTHOR

Antti Karttunen, Aug 29 2018

STATUS

approved

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Last modified May 21 08:53 EDT 2019. Contains 323441 sequences. (Running on oeis4.)