The On-Line Encyclopedia of Integer Sequences (OEIS)

The OEIS is supported by the many generous donors to the OEIS Foundation.

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give

A350068 revision #11

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

(list; graph; refs; listen; history; text; internal format)

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

Antti Karttunen, Table of n, a(n) for n = 1..10000 (based on Hans Havermann's factorization of A156552)

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, A300226, 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

proposed