

A305897


Filter sequence for prime factorization patterns, including also information about gaps between prime factors.


5



1, 2, 2, 3, 2, 4, 2, 5, 3, 6, 2, 7, 2, 8, 4, 9, 2, 10, 2, 11, 6, 12, 2, 13, 3, 14, 5, 15, 2, 16, 2, 17, 8, 18, 4, 19, 2, 20, 12, 21, 2, 22, 2, 23, 7, 24, 2, 25, 3, 26, 14, 27, 2, 28, 6, 29, 18, 30, 2, 31, 2, 32, 11, 33, 8, 34, 2, 35, 20, 36, 2, 37, 2, 38, 10, 39, 4, 40, 2, 41, 9, 42, 2, 43, 12, 44, 24, 45, 2, 46, 6, 47, 30, 48, 14, 49, 2, 50, 15, 51, 2, 52, 2, 53, 16
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OFFSET

1,2


COMMENTS

Restricted growth sequence transform of A246277.
For all i, j:
a(i) = a(j) => A077462(i) = A077462(j) => A101296(i) = A101296(j).
a(i) = a(j) => A243055(i) = A243055(j).


LINKS

Antti Karttunen, Table of n, a(n) for n = 1..100000


EXAMPLE

a(10) = a(21) (= 6) because both have prime exponents [1, 1] and the gap between prime factors is the same, as 10 = prime(1)*prime(3), and 21 = prime(2)*prime(4).
a(12) != a(18) because the prime exponents [2,1] and [1,2] do not occur in the same order.
a(140) = a(693) (= 71) because both numbers have prime exponents [2, 1, 1] (in this order) and the gaps between successive prime factors are same: 140 = prime(1)^2 * prime(3) * prime(4), 693 = prime(2)^2 * prime(4) * prime(5).


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; };
A246277(n) = if(1==n, 0, my(f = factor(n), k = primepi(f[1, 1])1); for (i=1, #f~, f[i, 1] = prime(primepi(f[i, 1])k)); factorback(f)/2);
v305897 = rgs_transform(vector(up_to, n, A246277(n)));
A305897(n) = v305897[n];


CROSSREFS

Cf. A077462, A101296, A246277, A300247, A305800.
Cf. also A286621.
Sequence in context: A129294 A323914 A300230 * A300248 A300247 A318887
Adjacent sequences: A305894 A305895 A305896 * A305898 A305899 A305900


KEYWORD

nonn


AUTHOR

Antti Karttunen, Jun 14 2018


STATUS

approved



