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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. 7
 15, 19, 21, 22, 23, 27, 28, 29, 30, 31, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The idea for this sequence comes from the French 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". It is possible to generalize for "k-phile" or "k-phobe" numbers (see Crossrefs). Some results: The smallest tetraphile number is 15 = 1 + 2 + 4 + 8 and the largest tetraphobe is 48, so this sequence is infinite since every integer >= 49 is a term. 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. There exist 23 tetraphobe numbers. LINKS Table of n, a(n) for n=1..69. Diophante, A496 - Pentaphiles et pentaphobes (in French). EXAMPLE As 22 = 1 + 3 + 6 + 12, 22 is a term. As 33 = 1 + 2 + 6 + 24, 33 is another term. MATHEMATICA Select[Range@92, Select[Select[IntegerPartitions[#, {4}], Length@Union@#==4&], And@@(IntegerQ/@Divide@@@Partition[#, 2, 1])&]!={}&] (* Giorgos Kalogeropoulos, Oct 22 2021 *) CROSSREFS k-phile numbers: A160811 \ {5} (k=3), this sequence (k=4), A348518 (k=5). k-phobe numbers: A019532 (k=3). Sequence in context: A167322 A217406 A181664 * A224535 A225861 A329184 Adjacent sequences: A348514 A348515 A348516 * A348518 A348519 A348520 KEYWORD nonn AUTHOR Bernard Schott, Oct 21 2021 STATUS approved

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Last modified September 26 08:38 EDT 2023. Contains 365654 sequences. (Running on oeis4.)