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A340346 The largest divisor of n that is a term of A055932 (numbers divisible by all primes smaller than their largest prime factor). 4
1, 2, 1, 4, 1, 6, 1, 8, 1, 2, 1, 12, 1, 2, 1, 16, 1, 18, 1, 4, 1, 2, 1, 24, 1, 2, 1, 4, 1, 30, 1, 32, 1, 2, 1, 36, 1, 2, 1, 8, 1, 6, 1, 4, 1, 2, 1, 48, 1, 2, 1, 4, 1, 54, 1, 8, 1, 2, 1, 60, 1, 2, 1, 64, 1, 6, 1, 4, 1, 2, 1, 72, 1, 2, 1, 4, 1, 6, 1, 16, 1, 2, 1, 12 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
LINKS
FORMULA
For n >= 1, a(2n-1) = 1, a(2n) = A006519(2n) * A003961(a(A064989(2n))).
For n >= 1, lcm(A006519(n), A234959(n)) | a(n).
EXAMPLE
For n=2: the largest divisor of 2 is 2, and 2 qualifies as divisible by all primes smaller than its largest prime factor, 2 (since there are no smaller primes). So a(2) = 2.
For n=42: of 42's divisors, no multiples of 7 qualify as being divisible by all primes smaller than their largest prime factor (since that factor is 7 and no divisor of 42 is divisible by 5, a smaller prime). The largest of 42's other divisors is 6, which qualifies (since it is divisible by 2, the only prime smaller than 6's largest prime factor, 3). So a(42) = 6.
MATHEMATICA
a[_?OddQ] = 1; a[n_] := Module[{f = FactorInteger[n]}, ind = Position[PrimePi /@ First /@ f - Range @ Length[f], _?(# > 0 &)]; If[ind == {}, n, Times @@ Power @@@ f[[1 ;; ind[[1, 1]] - 1]]]]; Array[a, 100] (* Amiram Eldar, Jan 14 2021 *)
PROG
(PARI) is(n) = my(f=factor(n)[, 1]~); f==primes(#f); \\ A055932
a(n) = vecmax(select(is, divisors(n))); \\ Michel Marcus, Jan 19 2021
(PARI)
A341629(n) = if(1==n, 1, my(f=factor(n)[, 1]~); (primepi(f[#f])==#f));
A340346(n) = fordiv(n, d, if(A341629(n/d), return(n/d))); \\ Antti Karttunen, Feb 25 2021
CROSSREFS
A003961, A006519, A055932, A064989, A341629 are used in a definition of this sequence.
Sequences with related definitions: A327832, A328479.
Cf. A234959.
Sequence in context: A161510 A329379 A328479 * A193267 A327832 A083258
KEYWORD
nonn,easy
AUTHOR
Peter Munn, Jan 04 2021
STATUS
approved

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Last modified April 23 15:20 EDT 2024. Contains 371916 sequences. (Running on oeis4.)