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A305891 Filter sequence combining 2-adic valuation (A007814) and the prime signature (A046523) of n. 8
1, 2, 3, 4, 3, 5, 3, 6, 7, 5, 3, 8, 3, 5, 9, 10, 3, 11, 3, 8, 9, 5, 3, 12, 7, 5, 13, 8, 3, 14, 3, 15, 9, 5, 9, 16, 3, 5, 9, 12, 3, 14, 3, 8, 17, 5, 3, 18, 7, 11, 9, 8, 3, 19, 9, 12, 9, 5, 3, 20, 3, 5, 17, 21, 9, 14, 3, 8, 9, 14, 3, 22, 3, 5, 17, 8, 9, 14, 3, 18, 23, 5, 3, 20, 9, 5, 9, 12, 3, 24, 9, 8, 9, 5, 9, 25, 3, 11, 17, 16, 3, 14, 3, 12, 26, 5, 3, 27, 3 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Restricted growth sequence transform of A286161, of the ordered pair [A007814(n), A046523(n)].

For all i, j: a(i) = a(j) => A291761(i) = A291761(j).

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..65537

PROG

(PARI)

up_to = 65537;

rgs_transform(invec) = { my(om = Map(), outvec = vector(length(invec)), u=1); for(i=1, length(invec), if(mapisdefined(om, invec[i]), my(pp = mapget(om, invec[i])); outvec[i] = outvec[pp] , mapput(om, invec[i], i); outvec[i] = u; u++ )); outvec; };

A007814(n) = valuation(n, 2);

A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ From A046523

Aux305891(n) = [A007814(n), A046523(n)];

v305891 = rgs_transform(vector(up_to, n, Aux305891(n)));

A305891(n) = v305891[n];

CROSSREFS

Cf. A286161, A291761, A305801.

Cf. also A305893.

Sequence in context: A322809 A291761 A319337 * A319347 A318888 A323079

Adjacent sequences:  A305888 A305889 A305890 * A305892 A305893 A305894

KEYWORD

nonn

AUTHOR

Antti Karttunen, Jun 14 2018

STATUS

approved

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Last modified October 19 11:00 EDT 2019. Contains 328216 sequences. (Running on oeis4.)