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A134865
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Numbers k meeting the following criterion: if k is a multiple of d, then it is also a multiple of the smallest number with same number of divisors as d.
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4
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1, 2, 4, 6, 12, 24, 36, 48, 120, 240, 360, 720, 2520, 5040, 7560, 10080, 15120, 20160, 45360, 50400, 100800, 332640, 352800, 665280, 705600, 4324320, 8648640, 17297280, 21621600, 43243200, 13492656777600
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OFFSET
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1,2
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COMMENTS
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Note that this is not a subsequence of A002182: 100800 is in this sequence but not in A002182. - J. Lowell, Feb 22 2008
A number k is in this sequence iff for every divisor d of k, A005179(A000005(d)) (= A140635(d)) is also a divisor of k. So the question of the finiteness of this sequence is closely related to the form of the elements of A005179. - Max Alekseyev, May 19 2008, May 20 2008
A subsequence of A007416 which is a subsequence of A025487, so every term is primally tight and even (after the first term). Thus if d is a divisor of a term, then the least integer with the same prime signature as d (=A046523(d)) is also a divisor. So only the divisors that are in A025487 need be tested. - Ray Chandler
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LINKS
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FORMULA
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EXAMPLE
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60 is a multiple of 30 with 8 divisors, but not of 24 (the smallest number with 8 divisors) so 60 is not a term of this sequence.
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MATHEMATICA
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a = {}; For[n = 1, n < 10000, n++, b = Divisors[n]; c = 1; For[i = 1, i < Length[b] + 1, i++, j = 1; While[Length[Divisors[j]] < Length[Divisors[b[[i]]]], j++ ]; If[ ! Mod[n, j] == 0, c = 0]]; If[c == 1, AppendTo[a, n]]]; a (* Stefan Steinerberger, Feb 05 2008 *)
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PROG
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(PARI) isA134865(n)={ n%2 & return(n==1); fordiv(n, d, bigomega(d)>1 || next; nd=numdiv(d); for(k=4, d, numdiv(k)==nd || next; n%k & return; break)); 1 }
for(n=1, 10^7, if(isA134865(n), print1(n, ", "))); \\ R. J. Mathar, May 17 2008
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CROSSREFS
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KEYWORD
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more,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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