A174905 - OEIS

A174905

Numbers with no pair (d,e) of divisors such that d < e < 2*d.

1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 13, 14, 16, 17, 19, 21, 22, 23, 25, 26, 27, 29, 31, 32, 33, 34, 37, 38, 39, 41, 43, 44, 46, 47, 49, 50, 51, 52, 53, 55, 57, 58, 59, 61, 62, 64, 65, 67, 68, 69, 71, 73, 74, 76, 79, 81, 82, 83, 85, 86, 87, 89, 92, 93, 94, 95, 97, 98, 101, 103, 106

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OFFSET

1,2

COMMENTS

A174903(a(n)) = 0; complement of A005279;

sequences of powers of primes are subsequences;

a(n) = A129511(n) for n < 27, A129511(27) = 35 whereas a(27) = 37.

Also the union of A241008 and A241010 (see the link for a proof). - Hartmut F. W. Hoft, Jul 02 2015

In other words: numbers n with the property that all parts in the symmetric representation of sigma(n) have width 1. - Omar E. Pol, Dec 08 2016

Sequence A357581 shows the numbers organized in columns of a square array by the number of parts in their symmetric representation of sigma. - Hartmut F. W. Hoft, Oct 04 2022

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Hartmut F. W. Hoft, Proof that this sequence equals union of A241008 and A241010

MAPLE

filter:= proc(n)

local d, q;

d:= numtheory:-divisors(n);

min(seq(d[i+1]/d[i], i=1..nops(d)-1)) >= 2

end proc:

select(filter, [$1..1000]); # Robert Israel, Aug 08 2014

MATHEMATICA

(* it suffices to test adjacent divisors *)