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A300232 Restricted growth sequence transform of A286152, filter combining A051953(n) and A046523(n), cototient and the prime signature of n. 6
1, 2, 2, 3, 2, 4, 2, 5, 6, 7, 2, 8, 2, 9, 10, 11, 2, 12, 2, 12, 13, 14, 2, 15, 16, 17, 18, 19, 2, 20, 2, 21, 22, 23, 24, 25, 2, 26, 27, 28, 2, 29, 2, 30, 31, 32, 2, 33, 34, 35, 36, 37, 2, 38, 27, 39, 40, 41, 2, 42, 2, 43, 44, 45, 46, 47, 2, 48, 49, 47, 2, 50, 2, 51, 52, 53, 46, 54, 2, 55, 56, 57, 2, 58, 40, 59, 60, 61, 2, 62, 36, 63, 64, 65, 66, 67, 2, 68, 69 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

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

EXAMPLE

a(39) = a(55) (= 27) because both are nonsquare semiprimes (3*13 and 5*11), and both have cototient value 15 = 39 - phi(39) = 55 - phi(55).

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; };

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

A051953(n) = (n - eulerphi(n));

A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ This function from Charles R Greathouse IV, Aug 17 2011

A286152(n) = (2 + ((A051953(n)+A046523(n))^2) - A051953(n) - 3*A046523(n))/2;

write_to_bfile(1, rgs_transform(vector(up_to, n, A286152(n))), "b300232.txt");

CROSSREFS

Cf. A046523, A051953, A286152.

Cf. also A295885, A300223, A300224, A300226, A300229, A300230, A300231, A300233, A300235.

Sequence in context: A323240 A300229 A300825 * A300233 A293217 A329351

Adjacent sequences:  A300229 A300230 A300231 * A300233 A300234 A300235

KEYWORD

nonn

AUTHOR

Antti Karttunen, Mar 01 2018

STATUS

approved

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Last modified November 16 19:17 EST 2019. Contains 329201 sequences. (Running on oeis4.)