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A350068 revision #4

A350068

Lexicographically earliest infinite sequence such that a(i) = a(j) => A046523(i) = A046523(j) and A350063(i) = A350063(j), for all i, j >= 1.

1, 2, 2, 3, 2, 4, 2, 5, 3, 6, 2, 7, 2, 4, 4, 8, 2, 7, 2, 7, 6, 9, 2, 10, 3, 9, 5, 11, 2, 12, 2, 13, 4, 9, 4, 14, 2, 4, 9, 15, 2, 16, 2, 7, 7, 17, 2, 18, 3, 19, 9, 7, 2, 10, 6, 10, 9, 20, 2, 21, 2, 9, 7, 22, 4, 12, 2, 11, 4, 16, 2, 23, 2, 9, 7, 11, 4, 12, 2, 18, 8, 9, 2, 24, 9, 25, 17, 26, 2, 24, 6, 11, 20, 27, 9

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OFFSET

1,2

COMMENTS

Restricted growth sequence transform of the ordered pair [A046523(n), A350063(n)].

For all i, j >= 1: A305897(i) = A305897(j) => a(i) = a(j).

LINKS

Table of n, a(n) for n=1..95.

Index entries for sequences computed from indices in prime factorization

PROG

(PARI)

up_to = 3003;

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; };

A000265(n) = (n>>valuation(n, 2));

A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); }; \\ From A046523

A156552(n) = { my(f = factor(n), p, p2 = 1, res = 0); for(i = 1, #f~, p = 1 << (primepi(f[i, 1]) - 1); res += (p * p2 * (2^(f[i, 2]) - 1)); p2 <<= f[i, 2]); res };

A350063(n) = if(1==n, 0, A046523(A000265(A156552(n))));

Aux350068(n) = [A046523(n), A350063(n)];

v350068 = rgs_transform(vector(up_to, n, Aux350068(n)));

A350068(n) = v350068[n];

CROSSREFS

Cf. A000265, A046523, A156552, A322993, A350063.

Cf. A000040 (positions of 2's), A001248 (of 3's).

Cf. also A101296, A305897, A350065.

Sequence in context: A363723 A350126 A323914 * A378603 A378601 A378602

Adjacent sequences: A350065 A350066 A350067 * A350069 A350070 A350071

KEYWORD

nonn

AUTHOR

Antti Karttunen, Jan 29 2022

STATUS

editing