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A060735 Where n / (phi(n) + 1) increases. 22
1, 2, 4, 6, 12, 18, 24, 30, 60, 90, 120, 150, 180, 210, 420, 630, 840, 1050, 1260, 1470, 1680, 1890, 2100, 2310, 4620, 6930, 9240, 11550, 13860, 16170, 18480, 20790, 23100, 25410, 27720, 30030, 60060, 90090, 120120, 150150, 180180, 210210 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Except for the initial 1, this sequence is a primorial (A002110) followed by its multiples until the next primorial, then the multiples of that primorial and so on. - Wilfredo Lopez (chakotay147138274(AT)yahoo.com), Dec 28 2006

a(1)=1, a(2)=2. For n >=3, a(n) = the smallest integer that both is > a(n-1) and is divisible by every prime that LCM(a(1),a(2),a(3),...a(n)) is divisible by. - Leroy Quet, Feb 23 2010

Numbers n for which A053589(n) = A260188(n), thus numbers with only one nonzero digit when written in primorial base A049345. - Antti Karttunen, Aug 30 2016

LINKS

Enrique Pérez Herrero, Table of n, a(n) for n = 1..5000

Michel Planat, Riemann hypothesis from the Dedekind psi function, arXiv:1010.3239 [math.GM], 2010.

Index entries for sequences related to primorial base

FORMULA

a(1) = 1, a(n) = a(n-1) + rad(a(n-1)) with rad=A007947, squarefree kernel. - Reinhard Zumkeller, Apr 10 2006

a(A101301(n)+1) = A002110(n). - Enrique Pérez Herrero, Jun 10 2012

MAPLE

seq(seq(k*mul(ithprime(i), i=1..n-1), k=1..ithprime(n)-1), n=1..10); # Vladeta Jovovic, Apr 08 2004

a := proc(n) option remember; if n=1 then return 1 fi; a(n-1);

% + convert(numtheory:-factorset(%), `*`) end:

seq(a(n), n=1..42); # after Zumkeller, Peter Luschny, Aug 30 2016

MATHEMATICA

a = 0; Do[ b = n/(EulerPhi[ n ] + 1); If[ b > a, a = b; Print[ n ] ], {n, 1, 10^6} ]

f[n_] := Range[Prime[n + 1] - 1] Times @@ Prime@ Range@ n;  Array[f, 7, 0] // Flatten (* Robert G. Wilson v, Jul 22 2015 *)

PROG

(PARI) first(n)=my(v=vector(n), k=1, p=1, P=1); v[1]=1; for(i=2, n, v[i]=P*k++; if(k>p && isprime(k), p=k; P=v[i]; k=1)); v \\ Charles R Greathouse IV, Jul 22 2015

CROSSREFS

Cf. A000010, A002110, A049345, A055719, A101301, A053589, A260188.

Indices of ones in A276157 and A267263.

Sequence in context: A072121 A175305 A171923 * A181416 A225566 A273009

Adjacent sequences:  A060732 A060733 A060734 * A060736 A060737 A060738

KEYWORD

nonn

AUTHOR

Robert G. Wilson v, Apr 23 2001

EXTENSIONS

Definition corrected by Franklin T. Adams-Watters, Apr 16 2009

STATUS

approved

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Last modified December 11 08:42 EST 2016. Contains 279044 sequences.