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A228382
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Abundant numbers that differ from the next abundant number by 3.
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6
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942, 945, 1572, 1575, 2202, 2205, 2832, 2835, 3462, 3465, 4092, 4095, 4722, 4725, 5352, 5355, 5772, 5985, 6432, 6435, 6612, 6615, 6822, 6825, 7242, 7245, 7425, 7872, 7875, 8082, 8085, 8412, 8415, 8502, 8505, 8922, 8925, 9132, 9135, 9552, 9555, 9762, 9765
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OFFSET
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1,1
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COMMENTS
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Apparently these numbers come up mostly by pairs m, m+3 with m even; the odd terms being a subsequence of A005231. But this is not always the case (e.g., note the term 7425).
The numbers of terms not exceeding 10^k, for k = 3, 4, ..., are 2, 43, 393, 3635, 37599, 374092, 3731903, 37338208, 373256850, ... . Apparently, the asymptotic density of this sequence exists and equals 0.00373... . - Amiram Eldar, May 30 2023
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LINKS
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EXAMPLE
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942 is abundant, 943 and 944 are deficient, 945 is abundant.
945 is abundant, 946 and 947 are deficient, 948 is abundant.
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MAPLE
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with(numtheory): select(n->sigma(n)>2*n and sigma(n+1)<2*(n+1) and sigma(n+2)<2*(n+2) and sigma(n+3)>2*(n+3), [$1..12000]); # Muniru A Asiru, Jun 09 2018
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MATHEMATICA
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With[{abs = Select[Range[10000], DivisorSigma[-1, #] > 2 &]}, abs[[Position[Differences[abs], 3] // Flatten]]] (* Amiram Eldar, May 30 2023 *)
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PROG
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(PARI) isok(n) = (sigma(n)> 2*n) && (sigma(n+1)< 2*(n+1)) && (sigma(n+2) < 2*(n+2)) && (sigma(n+3) > 2*(n+3)); \\ Michel Marcus, Aug 21 2013
(GAP) a:=Filtered([1..130000], n->Sigma(n)>2*n and Sigma(n+1)<2*(n+1) and Sigma(n+2)<2*(n+2) and Sigma(n+3)>2*(n+3)); # Muniru A Asiru, Jun 09 2018
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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