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 A300240 Filter sequence combining A009195(n) and A046523(n), i.e., gcd(n,phi(n)) and the prime signature of n. 5
 1, 2, 2, 3, 2, 4, 2, 5, 6, 4, 2, 7, 2, 4, 8, 9, 2, 10, 2, 7, 11, 4, 2, 12, 13, 4, 14, 7, 2, 15, 2, 16, 8, 4, 8, 17, 2, 4, 11, 12, 2, 18, 2, 7, 19, 4, 2, 20, 21, 22, 8, 7, 2, 23, 24, 12, 11, 4, 2, 25, 2, 4, 26, 27, 8, 15, 2, 7, 8, 15, 2, 28, 2, 4, 29, 7, 8, 18, 2, 20, 30, 4, 2, 31, 8, 4, 8, 12, 2, 32, 8, 7, 11, 4, 8, 33, 2, 34, 19, 35, 2, 15, 2, 12, 36 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Restricted growth sequence transform of P(A009195(n), A046523(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 6 and 10 are nonsquare semiprimes, and A009195(6) = A009195(10) = 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])); } A009195(n) = gcd(n, eulerphi(n)); A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ From A046523 Aux300240(n) = (1/2)*(2 + ((A046523(n)+A009195(n))^2) - A046523(n) - 3*A009195(n)); write_to_bfile(1, rgs_transform(vector(65537, n, Aux300240(n))), "b300240.txt"); CROSSREFS Cf. A009195, A046523. Cf. also A300230, A300241, A300242, A300243. Sequence in context: A300226 A300246 A329620 * A323168 A335425 A328113 Adjacent sequences:  A300237 A300238 A300239 * A300241 A300242 A300243 KEYWORD nonn AUTHOR Antti Karttunen, Mar 02 2018 STATUS approved

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Last modified July 24 18:34 EDT 2021. Contains 346273 sequences. (Running on oeis4.)