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A319709 Filter sequence combining primorial base representations of the proper divisors of n; Restricted growth sequence transform of A319708. 2
1, 2, 2, 3, 2, 4, 2, 5, 6, 7, 2, 8, 2, 9, 10, 11, 2, 12, 2, 13, 14, 15, 2, 16, 4, 17, 18, 19, 2, 20, 2, 21, 22, 23, 18, 24, 2, 25, 26, 27, 2, 28, 2, 29, 30, 31, 2, 32, 33, 34, 12, 35, 2, 36, 37, 38, 39, 40, 2, 41, 2, 42, 43, 44, 45, 46, 2, 47, 48, 49, 2, 50, 2, 51, 52, 53, 45, 54, 2, 55, 56, 57, 2, 58, 59, 60, 61, 62, 2, 63, 64, 65, 66, 67, 68, 69, 2, 70, 71 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

For all i, j:

  a(i) = a(j) => A001065(i) = A001065(j),

  a(i) = a(j) => A319713(i) = A319713(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; };

A276086(n) = { my(i=0, m=1, pr=1, nextpr); while((n>0), i=i+1; nextpr = prime(i)*pr; if((n%nextpr), m*=(prime(i)^((n%nextpr)/pr)); n-=(n%nextpr)); pr=nextpr); m; };

A319708(n) = { my(m=1); fordiv(n, d, if(d<n, m *= A276086(d))); (m); };

v319709 = rgs_transform(vector(up_to, n, A319708(n)));

A319709(n) = v319709[n];

CROSSREFS

Cf. A276086, A319708, A319713.

Cf. A293215, A293226, A300835 for similar constructions for other bases.

Sequence in context: A300232 A300233 A293217 * A293226 A328315 A327970

Adjacent sequences:  A319706 A319707 A319708 * A319710 A319711 A319712

KEYWORD

nonn

AUTHOR

Antti Karttunen, Oct 03 2018

STATUS

approved

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Last modified October 18 07:19 EDT 2019. Contains 328146 sequences. (Running on oeis4.)