A171936 -id:A171936 - cp's OEIS frontend

A171937 Forward van Eck transform of A000005.

0, 1, 2, 5, 2, 2, 4, 2, 16, 4, 2, 6, 4, 1, 6, 65, 2, 2, 4, 8, 1, 4, 6, 6, 24, 1, 6, 4, 2, 10, 6, 12, 1, 1, 3, 64, 4, 1, 7, 2, 2, 12, 4, 1, 5, 5, 6, 32, 72, 2, 4, 11, 6, 2, 2, 10, 1, 4, 2, 12, 6, 3, 5, 665, 4, 4, 4, 7, 5, 8, 2, 12, 6, 3, 1, 16, 5, 10, 4, 32, 544, 3, 6, 6, 1, 1, 4, 14, 8, 6, 2, 6, 1, 1, 11

Offset: 1

N. J. A. Sloane, Oct 24 2010

nonn

Least positive k such that d(n) = d(n+k), or 0 if no such k exists (d = A000005). - Altug Alkan, Jul 29 2016

Michael De Vlieger, Table of n, a(n) for n = 1..10001
N. J. A. Sloane, Transforms

Cf. A000005, A171936.

Cf. A079427.

{0}~Join~Array[Block[{k = 1}, While[DivisorSigma[0, #] != DivisorSigma[0, # + k], k++]; k] &, 94, 2] (* Michael De Vlieger, Aug 19 2021 *)

a(n) = if (n==1, 0, my(m=1, nd=numdiv(n)); while(numdiv(n+m) != nd, m++); m); \\ Michel Marcus, Sep 14 2021

a(n) = A079427(n) - n. - Ridouane Oudra, Sep 14 2021

A171934 Backwards van Eck transform of A000010.

Original entry on oeis.org

0, 1, 0, 1, 0, 2, 0, 3, 2, 2, 0, 2, 0, 5, 0, 1, 0, 4, 0, 4, 8, 11, 0, 4, 0, 5, 8, 2, 0, 6, 0, 15, 8, 2, 0, 8, 0, 11, 4, 6, 0, 6, 0, 11, 6, 23, 0, 8, 6, 6, 0, 7, 0, 16, 14, 4, 20, 29, 0, 12, 0, 31, 6, 13, 0, 16, 0, 4, 0, 14, 0, 2, 0, 11, 20, 2, 16, 6, 0, 12, 0, 7, 0, 6, 0, 37, 0, 6, 0, 6, 18, 23, 16, 47

Offset: 1

N. J. A. Sloane, Oct 24 2010

nonn

Given a sequence a, the backwards van Eck transform b is defined as follows: If a(n) has already appeared in a, let a(m) be the most recent occurrence, and set b(n)=n-m; otherwise b(n)=0. (Comment from A171899).

Antti Karttunen, Table of n, a(n) for n = 1..16384
Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537
N. J. A. Sloane, Transforms

Cf. A000010.

Cf. also A081373, A171899, A171900, A171932, A171933, A171936, A171941.

Block[{a = Array[EulerPhi, 94], b = {}, m}, Do[If[! IntegerQ[m[#]], Set[m[#], i]; AppendTo[b, 0], AppendTo[b, i - m[#]]; Set[m[#], i]] &@ a[[i]], {i, Length[a]}]; b] (* Michael De Vlieger, Apr 06 2021 *)

up_to = 105;
backVanEck_transform(invec) = { my(om = Map(), outvec = vector(length(invec)), u=1); for(i=1, length(invec), if(mapisdefined(om,invec[i]), my(pp = mapget(om, invec[i])); outvec[i] = i-pp, outvec[i] = 0); mapput(om,invec[i],i)); outvec; };
v171934 = backVanEck_transform(vector(up_to,n,eulerphi(n)));
A171934(n) = v171934[n]; \\ Antti Karttunen, Apr 06 2021

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A171937 Forward van Eck transform of A000005.

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