The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A348517

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A348517

Positive integers m with the property that there are 4 positive integers b_1 < b_2 < b_3 < b_4 such that b_1 divides b_2, b_2 divides b_3, b_3 divides b_4, and m = b_1 + b_2 + b_3 + b_4.
(history; published version)

#16 by N. J. A. Sloane at Fri Oct 22 23:52:22 EDT 2021

STATUS

editing

approved

#15 by N. J. A. Sloane at Fri Oct 22 23:51:55 EDT 2021

NAME

Positive integers m such with the property that there are 4 positive integers b_1 < b_2 < b_3 < b_4 such that b_1 divides b_2, b_2 divides b_3, b_3 divides b_4 , and m = b_1 + b_2 + b_3 + b_4.

STATUS

proposed

editing

Discussion

Fri Oct 22

23:52

N. J. A. Sloane: I also added the "Oxford comma"

#14 by Giorgos Kalogeropoulos at Fri Oct 22 15:38:19 EDT 2021

STATUS

editing

proposed

Discussion

Fri Oct 22

17:07

Bernard Schott: Thanks for improvements and program.

23:51

N. J. A. Sloane: To avoid the double "such that", you can say "with the property that" for the first one. I will demonstrate!

#13 by Giorgos Kalogeropoulos at Fri Oct 22 15:38:13 EDT 2021

MATHEMATICA

Select[Range@92, Select[Select[IntegerPartitions[#, {4}], Length@Union@#==4&], And@@(IntegerQ/@Divide@@@Partition[#, 2, 1])&]!={}&] (* Giorgos Kalogeropoulos, Oct 22 2021 *)

STATUS

proposed

editing

#12 by Wesley Ivan Hurt at Thu Oct 21 18:03:45 EDT 2021

STATUS

editing

proposed

#11 by Wesley Ivan Hurt at Thu Oct 21 18:03:06 EDT 2021

COMMENTS

The idea of for this sequence comes from the French site website Diophante (see link) where these numbers are called “tetraphile” or “4-phile”. A number that is not tetraphile is called "tetraphobe" or "4-phobe".

The smallest tetraphile number is 15 = 1 + 2 + 4 + 8 and the largest tetraphobe is 48, so this sequence is infinite since all every integer >= 49 is a term.

STATUS

proposed

editing

#10 by Bernard Schott at Thu Oct 21 17:57:58 EDT 2021

STATUS

editing

proposed

#9 by Bernard Schott at Thu Oct 21 17:57:11 EDT 2021

COMMENTS

The smallest tetraphile number is 15 = 1 + 2 + 4 + 8 and the largest tetraphobe is 48, so, this sequence is infinite since all integer >= 49 is a term.

There exist 23 tetraphobe numbers.

EXAMPLE

As 34 33 = 1 + 2 + 6 + 24, 33 is another term.

STATUS

proposed

editing

#8 by Bernard Schott at Thu Oct 21 07:59:42 EDT 2021

STATUS

editing

proposed

#7 by Bernard Schott at Thu Oct 21 07:20:57 EDT 2021

COMMENTS

If m is tetraphile, q* m, q > 1, is another tetraphile number.

Numbers equal to 1 + 2*triphile (A160811) are tetraphile, numbers, but there are other terms not of this form, as even terms.