OFFSET

1,2

COMMENTS

For all i, j:

LINKS

EXAMPLE

Numbers 2 (= 2^1), 3 (= 3^1), 6 = (2^1 * 3^1) and 30 (2^1 * 3^1 * 5^1) all have just one distinct exponent, 1, in the multisets of exponents that occur in their prime factorization, thus they all have the same value a(2) = a(3) = a(6) = a(30) = 2 in this sequence.

Number 4 (2^2), 9 (3^2) and 36 (2^2 * 3^2) all have just one distinct exponent, 2, in the multisets of exponents that occur in their prime factorization, thus they all have the same value a(4) = a(9) = a(36) = 3 in this sequence.

Numbers 12 = 2^2 * 3^1, 18 = 2^1 * 3^2, 60 = 2^2 * 3^1 * 5^1 and 300 = 2^2 * 3^1 * 5^2 all have both 1 and 2 and none other values occurring in the multisets of exponents in their prime factorization, thus they all have the value of a(12) = 5 that was allotted to 12 by the restricted growth sequence transform, as 12 is the smallest number with prime signature (1, 2).

PROG

(PARI)

up_to = 100000;

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; };

A007947(n) = factorback(factorint(n)[, 1]);

A181819(n) = factorback(apply(e->prime(e), (factor(n)[, 2])));

A328401(n) = v328401[n];

CROSSREFS

KEYWORD

nonn

AUTHOR

Antti Karttunen, Oct 17 2019

STATUS

approved