A240521 a(n) = A050376(n)*A050376(n+1) where A050376(n) is the n-th number of the form p^(2^k) with p is prime and k >= 0.

6, 12, 20, 35, 63, 99, 143, 208, 272, 323, 437, 575, 725, 899, 1147, 1517, 1763, 2021, 2303, 2597, 3127, 3599, 4087, 4757, 5183, 5767, 6399, 6723, 7387, 8633, 9797, 10403, 11021, 11663, 12317, 13673, 15367, 16637, 17947, 19043, 20711, 22499, 23707, 25591

Offset

1,1

Comments

Let m be an odd positive number. Let S_m denote the sequence {Product_{i=1..r} q_(n+t_i)}_{n>=1}, where {q_i} is sequence A050376 and Sum_{i=1..r} 2^(t_1 - t_i) is the binary representation of m, such that t_1 > t_2 > ... > t_r = 0. Note that {S_1, S_3, S_5, ...} is a partition of all integers > 1. Then S_1=A050376, which is obtained when we set r=1, t_1 = 0. [Formula made compatible with A240535 data by Peter Munn, Aug 10 2021]

This present sequence is S_3 in this partition. It is obtained when we set r=2, t_1=1, t_2=0.

S_m(n) = A052330(A030101(m)*2^(n-1)) = A329330(A050376(n), A052330(A030101(m))). - Peter Munn, Aug 10 2021

A minimal set of generators for A000379 as a group under A059897(.,.). - Peter Munn, Aug 11 2019

Links

Table of n, a(n) for n=1..44.

Eric Weisstein's World of Mathematics, Group.

Wikipedia, Generating set of a group.

Formula

a(n) = A052330(3*2^(n-1)) = A329330(A050376(n), 6). - Peter Munn, Aug 10 2021

Crossrefs

Positions of 3's in A240535.

Sequences for other parts of the partition described in the first comment: A050376 (S_1), A240522 (S_5), A240524 (S_7), A240536 (S_9), A241024 (S_11), A241025 (S_13).

Cf. A000379, A030101, A052330, A059897, A329330.

Sequence in context: A309836 A117343 A286290 * A366928 A220211 A028611

Adjacent sequences: A240518 A240519 A240520 * A240522 A240523 A240524

Keyword

nonn

Author

Vladimir Shevelev, Apr 07 2014

Extensions

More terms from Peter J. C. Moses, Apr 18 2014

Status

approved