The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A284009

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A284009

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

#12 by N. J. A. Sloane at Thu Mar 23 14:40:27 EDT 2017

STATUS

proposed

approved

#11 by Antti Karttunen at Thu Mar 23 12:22:19 EDT 2017

STATUS

editing

proposed

#10 by Antti Karttunen at Thu Mar 23 12:21:53 EDT 2017

FORMULA

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

KEYWORD

nonn,look,new

STATUS

approved

editing

Discussion

Thu Mar 23

12:22

Antti Karttunen: More Sagrada Familias... This one is fine.

#9 by N. J. A. Sloane at Thu Mar 23 11:45:10 EDT 2017

STATUS

proposed

approved

#8 by Indranil Ghosh at Wed Mar 22 15:47:41 EDT 2017

STATUS

editing

proposed

#7 by Indranil Ghosh at Wed Mar 22 15:47:01 EDT 2017

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 *)

#6 by Indranil Ghosh at Wed Mar 22 15:45:54 EDT 2017

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 *)

STATUS

proposed

editing

#5 by Antti Karttunen at Wed Mar 22 14:35:52 EDT 2017

STATUS

editing

proposed

#4 by Antti Karttunen at Wed Mar 22 14:34:18 EDT 2017

LINKS

Antti Karttunen, <a href="/A284009/b284009.txt">Table of n, a(n) for n = 0..8191</a>

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));

#3 by Antti Karttunen at Wed Mar 22 14:13:52 EDT 2017

NAME

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

FORMULA

Other identities. For all n >= 0:

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

CROSSREFS

Cf. A001222, A007306, A277328, A284008.