A300226 - OEIS

A300226

Filter sequence combining A046523(n) and A052126(n), the prime signature of n and n/(largest prime dividing n).

1, 2, 2, 3, 2, 4, 2, 5, 6, 4, 2, 7, 2, 4, 8, 9, 2, 10, 2, 7, 8, 4, 2, 11, 12, 4, 13, 7, 2, 14, 2, 15, 8, 4, 16, 17, 2, 4, 8, 11, 2, 14, 2, 7, 18, 4, 2, 19, 20, 21, 8, 7, 2, 22, 16, 11, 8, 4, 2, 23, 2, 4, 18, 24, 16, 14, 2, 7, 8, 25, 2, 26, 2, 4, 27, 7, 28, 14, 2, 19, 29, 4, 2, 23, 16, 4, 8, 11, 2, 30, 28, 7, 8, 4, 16, 31, 2, 32, 18, 33, 2, 14, 2, 11, 34

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OFFSET

1,2

COMMENTS

Restricted growth sequence transform of P(A046523(n), A052126(n)), where P(a,b) is a two-argument form of A000027 used as a Cantor pairing function N x N -> N.

LINKS

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

EXAMPLE

a(6) = a(10) (= 4) because both are nonsquare semiprimes (2*3 and 2*5), and when the largest prime factor is divided out, both yield the same quotient, 2.

PROG

(PARI)

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; };

write_to_bfile(start_offset, vec, bfilename) = { for(n=1, length(vec), write(bfilename, (n+start_offset)-1, " ", vec[n])); }

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

A052126(n) = if(1==n, n, my(f=factor(n)[, 1], gpf = f[#f]); n/gpf); \\ After code in A052126.

Aux300226(n) = (1/2)*(2 + ((A052126(n)+A046523(n))^2) - A052126(n) - 3*A046523(n));

write_to_bfile(1, rgs_transform(vector(65537, n, Aux300226(n))), "b300226.txt");

CROSSREFS

Cf. A046523, A052126.

Cf. also A291761, A300229.

Sequence in context: A355831 A300223 A351949 * A300246 A329620 A300240

Adjacent sequences: A300223 A300224 A300225 * A300227 A300228 A300229

KEYWORD

nonn

AUTHOR

Antti Karttunen, Mar 01 2018

STATUS

approved