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A343302
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Numbers k such that k through k+4 are all deficient (in A005100).
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4
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1, 7, 13, 31, 43, 49, 61, 73, 91, 115, 121, 127, 133, 145, 151, 163, 169, 181, 187, 211, 229, 235, 241, 247, 253, 265, 283, 289, 295, 313, 325, 331, 343, 355, 373, 385, 403, 409, 421, 427, 433, 451, 469, 481, 505, 511, 523, 535, 553, 565, 583, 589, 595
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OFFSET
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1,2
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COMMENTS
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Since every multiple of 6 (other than 6 itself) is an abundant number, the maximum length of consecutive runs of deficient numbers is 5.
All terms are congruent to 1 modulo 6.
This is a proper subset of A231626, with the smallest missing term being 347: here only the first members of 5 consecutive deficient numbers in arithmetic progression with common difference 1 are allowed. Terms of A231626 that are not here are listed in A343303.
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LINKS
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EXAMPLE
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115 is a term since all of 115, 116, 117, 118 and 119 are deficient.
2989 is not a term since 2989 + 3 = 2992 is an abundant number.
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MATHEMATICA
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Position[Partition[DivisorSigma[-1, Range[600]], 5, 1], _?(Max[#] < 2 &), 1] // Flatten (* Amiram Eldar, Mar 21 2024 *)
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PROG
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(PARI) isA343302(k) = if(k%6!=1, 0, for(i=0, 4, if( sigma(k+i) >= 2*(k+i), return(0) )); 1)
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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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