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A331752
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Numbers k such that squarefree part of sigma(k) is equal to squarefree part of 2*k.
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4
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6, 28, 468, 496, 775, 2268, 3780, 4655, 7448, 8128, 9000, 10880, 10976, 25137, 40131, 40176, 58752, 62775, 66960, 91000, 137541, 137940, 140800, 160930, 167400, 173600, 195938, 224450, 307125, 377055, 399360, 406224, 417477, 494832, 569184, 603288, 634725, 639158, 658368, 773175, 869022, 881280, 889056, 1005480
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OFFSET
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1,1
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COMMENTS
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Numbers k such that A007913(sigma(k)) is equal to A007913(2*k), thus numbers for which sigma(k) has the same set of distinct prime factors with an odd exponent as 2*k.
Among the first 257 terms, these four are also in A228058:
46277101 = 61 * 13^2 * 67^2,
49889853 = 13 * 3^2 * 653^2,
106706925 = 13 * 3^2 * 5^2 * 191^2,
676830973 = 37 * 7^2 * 13^2 * 47^2.
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LINKS
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EXAMPLE
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For n = 46277101 = 61 * 13^2 * 67^2, sigma(46277101) = 51703722 = 2 * 3^2 * 7^2 * 31^2 * 61, with A007913(sigma(46277101)) = 2*61 = A007913(2*46277101), thus 46277101 is included in this sequence.
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MATHEMATICA
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PROG
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(PARI) isA331752(n) = (core(2*n)==core(sigma(n)));
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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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