A065203 -id:A065203 - cp's OEIS frontend

A065204 Least m such that A065203(m) = n.

Original entry on oeis.org

1, 3, 22, 191, 2206, 29054, 497585

Offset: 1

Vladeta Jovovic, Oct 21 2001

Conjecture: A064413(a(n)) = A002110(n) (primorial numbers), i.e., a(n) sets positions of primorial numbers in A064413.

Cf. A064413, A064742, A065203, A002110.

a(6)-a(7) from Sean A. Irvine, Aug 21 2023

A278263 Least number with the same prime signature as the n-th term of EKG-sequence: a(n) = A046523(A064413(n)).

Original entry on oeis.org

1, 2, 4, 6, 2, 4, 12, 8, 6, 2, 6, 12, 6, 2, 6, 24, 16, 12, 6, 2, 6, 8, 30, 4, 6, 12, 6, 2, 6, 36, 32, 6, 2, 6, 30, 6, 2, 6, 12, 24, 12, 6, 2, 6, 48, 12, 12, 24, 24, 4, 12, 60, 6, 6, 30, 6, 2, 6, 30, 6, 2, 6, 72, 64, 12, 6, 2, 6, 12, 30, 12, 48, 6, 2, 6, 16, 60, 6, 24, 6, 2, 6, 60, 6, 6, 36, 12, 6, 2, 6, 96, 12, 6, 24, 30, 12, 30, 72, 6, 2, 6, 30, 30, 48, 12, 6

Offset: 1

Antti Karttunen, Nov 16 2016

nonn

This sequence works as a "sentinel" for EKG-sequence by matching to any sequence that is obtained as f(A064413(n)), where f(n) is any function that depends only on the prime signature of n (see the index entry for "sequences computed from exponents in ..."). The last line in Crossrefs section lists such sequences that were present in the database as of Nov 11 2016.

Terms and b-file computed from b-file of A064413 provided by Zak Seidov.

Antti Karttunen, Table of n, a(n) for n = 1..10000
Index entries for sequences computed from exponents in factorization of n

Cf. A046523, A064413, A278264.

Sequences that partition N into same or coarser equivalence classes: A064742, A065203.

(define (A278263 n) (A046523 (A064413 n)))

a(n) = A046523(A064413(n)).

A304113 Restricted growth sequence transform of A278263(n) = A046523(A064413(n)), a filter based on the prime signature of EKG-sequence.

Original entry on oeis.org

1, 2, 3, 4, 2, 3, 5, 6, 4, 2, 4, 5, 4, 2, 4, 7, 8, 5, 4, 2, 4, 6, 9, 3, 4, 5, 4, 2, 4, 10, 11, 4, 2, 4, 9, 4, 2, 4, 5, 7, 5, 4, 2, 4, 12, 5, 5, 7, 7, 3, 5, 13, 4, 4, 9, 4, 2, 4, 9, 4, 2, 4, 14, 15, 5, 4, 2, 4, 5, 9, 5, 12, 4, 2, 4, 8, 13, 4, 7, 4, 2, 4, 13, 4, 4, 10, 5, 4, 2, 4, 16, 5, 4, 7, 9, 5, 9, 14, 4, 2, 4, 9, 9, 12, 5

Offset: 1

Antti Karttunen, May 17 2018

nonn

For all i, j: a(i) = a(j) => A064742(i) = A064742(j).

For all i, j: a(i) = a(j) => A065203(i) = A065203(j).

Antti Karttunen, Table of n, a(n) for n = 1..65539
Index entries for sequences related to EKG sequence

Cf. A046523, A064413, A064742, A065203, A278263, A304112.

Cf. also A304115.

\\ Needs also code for A064413:
write_to_bfile(start_offset,vec,bfilename) = { for(n=1, length(vec), write(bfilename, (n+start_offset)-1, " ", vec[n])); }
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; };
A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ From A046523
A278263(n) = A046523(A064413(n));
write_to_bfile(1,rgs_transform(vector(65539,n,A278263(n))),"b304113.txt");

cp's OEIS Frontend

A065204 Least m such that A065203(m) = n.

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A278263 Least number with the same prime signature as the n-th term of EKG-sequence: a(n) = A046523(A064413(n)).

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A304113 Restricted growth sequence transform of A278263(n) = A046523(A064413(n)), a filter based on the prime signature of EKG-sequence.

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