A284009 - OEIS

A284009

Number of primes (counted with multiplicity) dividing lcm(A260443(n), A260443(n+1)): a(n) = A001222(A284008(n)).

1, 2, 2, 3, 4, 4, 3, 4, 5, 5, 6, 6, 6, 6, 4, 5, 6, 6, 8, 9, 10, 9, 8, 8, 8, 8, 9, 9, 8, 8, 5, 6, 7, 7, 10, 10, 13, 13, 11, 12, 13, 12, 15, 16, 14, 13, 10, 10, 10, 10, 13, 14, 15, 14, 12, 12, 11, 11, 12, 12, 10, 10, 6, 7, 8, 8, 12, 12, 15, 15, 14, 15, 17, 17, 20, 21, 20, 19, 14, 15, 16, 15, 21, 22, 24, 24, 20, 21, 20, 18, 21, 21, 17, 17, 12, 12, 12, 12, 17, 18

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OFFSET

0,2

LINKS

Antti Karttunen, Table of n, a(n) for n = 0..8191

FORMULA

a(n) = A001222(A284008(n)).

Other identities. For all n >= 0:

a(n) + A277328(n) = A007306(1+n).

MATHEMATICA

a[p_?PrimeQ] := a[p] = Prime[ PrimePi[p] + 1]; a[1] = 1; a[n_] := a[n] = Times @@ ( a[First[#]] ^ Last[#] & ) /@ FactorInteger[n]; (* after Jean-François Alcover, in A003961 *) A[n_]:= If[n<2, n + 1, If[EvenQ[n], a[A[n/2]], A[(n - 1)/2] A[(n + 1)/2]]] ; Table[A[n], {n, 0, 51}] (* sequence A260443 *) Table[PrimeOmega[LCM[A[n], A[n + 1]]], {n, 0, 101}] (* Indranil Ghosh, Mar 22 2017 *)

PROG

(PARI)

A003961(n) = my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); \\ From Michel Marcus

A260443(n) = if(n<2, n+1, if(n%2, A260443(n\2)*A260443(n\2+1), A003961(A260443(n\2))));

A284008(n) = lcm(A260443(n), A260443(1+n));

A284009(n) = bigomega(A284008(n));

(Scheme) (define (A284009 n) (A001222 (A284008 n)))

CROSSREFS

Cf. A001222, A007306, A277328, A284008.

Sequence in context: A243503 A069581 A274061 * A339695 A326846 A243220

Adjacent sequences: A284006 A284007 A284008 * A284010 A284011 A284012

KEYWORD

nonn,look

AUTHOR

Antti Karttunen, Mar 22 2017

STATUS

approved