A068626 -id:A068626 - cp's OEIS frontend

A068627 a(0) = 0, a(n) = a(n-1) + n if n does not divide a(n-1). a(n) = a(n-1) - n if n divides a(n-1). a(n) = n if a(n-1) = 0.

0, 1, 3, 0, 4, 9, 15, 22, 30, 39, 49, 60, 48, 61, 75, 60, 76, 93, 111, 130, 150, 171, 193, 216, 192, 217, 243, 216, 244, 273, 303, 334, 366, 399, 433, 468, 432, 469, 507, 468, 508, 549, 591, 634, 678, 723, 769, 816, 768, 817, 867, 816, 868, 921, 975, 1030, 1086

Offset: 0

Amarnath Murthy, Feb 26 2002

The sequence is not monotonically increasing but has an increasing trend with some nodes i.e. numbers occurring twice in the sequence like 60 etc. Are there infinitely many nodes in the sequence?

			Since 12 divides a(11)=60, a(12) = 60 - 12 = 48.
Since 13 does not divide a(12)=48, a(13) = 48 + 13 = 61.

Harvey P. Dale, Table of n, a(n) for n = 0..1000

Cf. A068626.

nxt[{n_,a_}]:={n+1,Which[a==0,n+1,Divisible[a,n+1],a-(n+1),True,a+n+1]}; NestList[nxt,{0,0},60][[All,2]] (* Harvey P. Dale, Jun 29 2021 *)

lista(nn) = {preca = 0; for (n=1, nn, print1(preca, ", "); if (preca == 0, nexta = n, if (preca % n, nexta = preca + n, nexta = preca - n);); preca = nexta;);} \\ Michel Marcus, Jan 23 2014

A068629 a(1) = 1. a(n) = n*a(n-1) if gcd(n,a(n-1)) = 1, a(n-1)/n if n divides a(n-1), otherwise a(n) = a(n-1).

Original entry on oeis.org

1, 2, 6, 6, 30, 5, 35, 280, 2520, 252, 2772, 231, 3003, 3003, 3003, 48048, 816816, 816816, 15519504, 15519504, 739024, 33592, 772616, 772616, 19315400, 742900, 20058300, 20058300, 581690700, 19389690, 601080390, 601080390

Offset: 1

Amarnath Murthy, Feb 26 2002

The sequence can also be obtained by taking a(1) = 1 and then multiplying the previous term by n if n is coprime to the previous term a(n-1), dividing the previous term by n if n divides the previous term a(n-1), taking a(n) = a(n-1) if n is unrelated to a(n-1). - Amarnath Murthy, Oct 30 2002 (corrected by Franklin T. Adams-Watters, Dec 13 2006)

Ivan Neretin, Table of n, a(n) for n = 1..1000

Cf. A034386, A068626, A068627, A068628.

a = {1}; Do[AppendTo[a, If[GCD[a[[-1]], n] == 1, a[[-1]]*n, If[Divisible[a[[-1]], n], a[[-1]]/n, a[[-1]]]]], {n, 2, 32}]; a (* Ivan Neretin, May 21 2015 *)

print1(k=1); for(n=2,99, if(gcd(k,n)==1, k*=n, if(k%n==0, k/=n)); print1(", "k)) \\ Charles R Greathouse IV, May 21 2015

a(26)-a(32) corrected by Ivan Neretin, May 21 2015

A115012 Sum_{i=1..n, gcd(5,i)=1} i.

Original entry on oeis.org

1, 3, 6, 10, 10, 16, 23, 31, 40, 40, 51, 63, 76, 90, 90, 106, 123, 141, 160, 160, 181, 203, 226, 250, 250, 276, 303, 331, 360, 360, 391, 423, 456, 490, 490, 526, 563, 601, 640, 640, 681, 723, 766, 810, 810, 856, 903, 951, 1000, 1000, 1051, 1103, 1156, 1210, 1210, 1266

Offset: 1

N. J. A. Sloane, Feb 24 2006

nonn

Replacing 5 in the definition by 2, 3, 4, 5, 6, 7, 8, 9 gives respectively A008794, A068626, A008794, this sequence, A115014, A115015, A008794, A068626.

A068630 a(0)=0; a(n) = n + a(n-1) if gcd(n,a(n-1)) = 1 or a(n-1) = 0; a(n) = a(n-1) - n if n divides a(n-1), otherwise a(n) = a(n-1).

Original entry on oeis.org

0, 1, 3, 0, 4, 9, 9, 16, 8, 17, 27, 38, 38, 51, 65, 65, 81, 98, 98, 117, 137, 158, 158, 181, 205, 205, 231, 231, 231, 260, 260, 291, 323, 356, 356, 391, 427, 464, 464, 503, 543, 584, 584, 627, 627, 627, 673, 720, 672, 672, 672, 672, 672, 725, 779, 834, 834, 834

Offset: 0

Amarnath Murthy, Feb 26 2002

Cf. A068626, A068627, A068628, A068629.

Offset and a(55)-a(57) corrected by Gionata Neri, Mar 23 2017

cp's OEIS Frontend

A068627 a(0) = 0, a(n) = a(n-1) + n if n does not divide a(n-1). a(n) = a(n-1) - n if n divides a(n-1). a(n) = n if a(n-1) = 0.

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A068629 a(1) = 1. a(n) = n*a(n-1) if gcd(n,a(n-1)) = 1, a(n-1)/n if n divides a(n-1), otherwise a(n) = a(n-1).

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A115012 Sum_{i=1..n, gcd(5,i)=1} i.

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A068630 a(0)=0; a(n) = n + a(n-1) if gcd(n,a(n-1)) = 1 or a(n-1) = 0; a(n) = a(n-1) - n if n divides a(n-1), otherwise a(n) = a(n-1).

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