A225640 -id:A225640 - cp's OEIS frontend

A225650 The greatest common divisor of Landau g(n) and n.

1, 1, 2, 3, 4, 1, 6, 1, 1, 1, 10, 1, 12, 1, 14, 15, 4, 1, 6, 1, 20, 21, 2, 1, 24, 5, 2, 1, 14, 1, 30, 1, 4, 3, 2, 35, 36, 1, 2, 39, 40, 1, 42, 1, 44, 15, 2, 1, 24, 7, 10, 3, 52, 1, 18, 55, 56, 3, 2, 1, 60, 1, 2, 21, 8, 65, 66, 1, 4, 3, 70, 1, 72, 1, 2, 15, 76, 77, 78, 1

Offset: 0

Antti Karttunen, May 11 2013

nonn

R. J. Mathar, Table of n, a(n) for n = 0..10000

A225648 gives the position of ones, and likewise A225651 gives the positions of fixed points, that is, a(A225651(n)) = A225651(n) for all n.

Cf. A225640-A225643, A225654.

b[n_, i_] := b[n, i] = Module[{p}, p = If[i < 1, 1, Prime[i]]; If[n == 0 || i < 1, 1, Max[b[n, i - 1], Table[p^j*b[n - p^j, i - 1], {j, 1, Log[p, n] // Floor}]]]]; g[n_] := b[n, If[n < 8, 3, PrimePi[Ceiling[1.328*Sqrt[n* Log[n] // Floor]]]]]; a[n_] := GCD[n, g[n]]; Table[a[n], {n, 0, 100}] (* Jean-François Alcover, Mar 02 2016, after Alois P. Heinz *)

(define (A225650 n) (gcd (A000793 n) n))
;; Scheme-code for A000793 can be found in the Program section of that entry.

a(n) = gcd(n, A000793(n)).

A225646 a(n) = lcm(n,p1,p2,...,pk) for such a partition of n which maximizes this value among all partitions {p1+p2+...pk} of n.

Original entry on oeis.org

1, 1, 2, 6, 12, 30, 30, 84, 120, 180, 210, 330, 420, 780, 630, 840, 1680, 3570, 1386, 7980, 1980, 4620, 6930, 19320, 9240, 23100, 30030, 41580, 16380, 73080, 10920, 143220, 110880, 120120, 157080, 120120, 180180, 512820, 311220, 240240, 360360, 1231230, 180180

Offset: 0

Antti Karttunen, May 15 2013

nonn

Second row of table A225640.

a(0)=1 by convention.

Index entries for sequences related to lcm's

Cf. A225640, A225642, A225652, A000793, A225655.

(define (A225646 n) (let ((maxlcm (list 1))) (fold_over_partitions_of n n lcm (lambda (p) (set-car! maxlcm (max (car maxlcm) p)))) (car maxlcm)))
(define (fold_over_partitions_of m initval addpartfun colfun) (let recurse ((m m) (b m) (n 0) (partition initval)) (cond ((zero? m) (colfun partition)) (else (let loop ((i 1)) (recurse (- m i) i (+ 1 n) (addpartfun i partition)) (if (< i (min b m)) (loop (+ 1 i))))))))

A225649 Positions of non-ones in A225650, numbers n such that n and A000793(n) have at least one common divisor > 1.

Original entry on oeis.org

2, 3, 4, 6, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 64, 65, 66, 68, 69, 70, 72, 74, 75, 76, 77, 78, 80, 81, 82, 84, 85, 86, 87, 88, 90, 91, 92

Offset: 1

Antti Karttunen, May 13 2013

nonn

Which composites are missing apart from 8, 9 and 27? See comment at A225648.

Cf. A225648 (complement), A225651 (from n>1 onward is a subset).

Cf. A225650, A225640.

cp's OEIS Frontend

A225650 The greatest common divisor of Landau g(n) and n.

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A225646 a(n) = lcm(n,p1,p2,...,pk) for such a partition of n which maximizes this value among all partitions {p1+p2+...pk} of n.

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A225649 Positions of non-ones in A225650, numbers n such that n and A000793(n) have at least one common divisor > 1.

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