

A160102


Multiplicative function, onetoone and onto the squarefree numbers.


1



1, 2, 3, 5, 7, 6, 11, 10, 13, 14, 17, 15, 19, 22, 21, 23, 29, 26, 31, 35, 33, 34, 37, 30, 41, 38, 39, 55, 43, 42, 47, 46, 51, 58, 77, 65, 53, 62, 57, 70, 59, 66, 61, 85, 91, 74, 67, 69, 71, 82, 87, 95, 73, 78, 119, 110, 93, 86, 79, 105, 83, 94, 143, 115, 133, 102, 89, 145
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OFFSET

1,2


COMMENTS

Multiplicative with a(A050376(m)) = Prime(m) = A000040(m). If k = 2^{i_1} + ... + 2^{i_j} is the binary representation of k, a(p^k) = a(p^2^{i_1}) * ... * a(p^2^{i_j}). [edited by Peter Munn, Jan 07 2020]
Equivalently, a(A050376(m)) = A000040(m); a(A059897(n,k)) = A059897(a(n), a(k)).  Peter Munn, Dec 30 2019


LINKS

Ivan Neretin, Table of n, a(n) for n = 1..10000


FORMULA

From Peter Munn, Dec 30 2019: (Start)
a(n) = A019565(A052331(n)).
a(A052330(k)) = A019565(k).
(End)


PROG

(PARI) al(n)={local(v, k, fm, m, p);
v=vector(n); v[1]=1; p=1;
for(k=2, n, fm=factor(k);
if(matsize(fm)[1]>1, m=fm[1, 1]^fm[1, 2]; v[k]=v[m]*v[k/m],
m=2^valuation(fm[1, 2], 2);
if(m==fm[1, 2], p=nextprime(p+1); v[k]=p,
m=fm[1, 1]^m; v[k]=v[m]*v[k/m])));
v}


CROSSREFS

Sequences used in definitions of this sequence: A000040, A019565, A050376, A052331, A059897.
Cf. A005117 (range of values), A052330.
Sequence in context: A126890 A122637 A076229 * A318954 A296375 A306923
Adjacent sequences: A160099 A160100 A160101 * A160103 A160104 A160105


KEYWORD

mult,nonn


AUTHOR

Franklin T. AdamsWatters, May 01 2009


STATUS

approved



