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A071628 Smallest m such that (2n-1)*2^m is totient, that is, in A002202. 2
1, 1, 1, 2, 1, 1, 2, 1, 3, 6, 1, 1, 2, 1, 1, 8, 1, 1, 2, 1, 1, 2, 2, 583, 2, 1, 1, 1, 2, 5, 4, 1, 1, 2, 1, 3, 2, 1, 3, 2, 1, 1, 4, 2, 1, 4, 2, 1, 2, 1, 3, 16, 1, 3, 6, 1, 1, 2, 2, 1, 4, 2, 1, 2, 3, 1, 4, 1, 3, 2, 1, 3, 2, 1, 3, 4, 1, 1, 8, 2, 3, 2, 1, 7, 2, 1, 1, 2, 2, 1, 4, 1, 3, 4, 1, 1, 2, 2, 15, 2, 3, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

When 2n-1 is the k-th prime, then a(n) = A040076(2n-1) = A046067(n) = A057192(k).

LINKS

T. D. Noe, Table of n, a(n) for n=1..1000

D. Bressoud, CNT.m Computational Number Theory Mathematica package.

FORMULA

a(n)=Min[{x; Card(InvPhi[(2n-1)*(2^x)])>0}]

EXAMPLE

n=52:2n-1=13, [seq(nops(invphi(103*2^i)),i=1..25)]; gives: [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,3,6,8,10,12,14,16,18,20]; nonzero appears first at position 16, so a(52)=16,since 6750208=103.2^16 is totient, while 3375104 is nontotient. n=24, 2n-1=47: the first nonempty InvPhi(47.2^i) set arises at i=a[24]=583, a very large number.

MAPLE

with(numtheory); [seq(nops(invphi(odd*2^i)), i=1..N)]; Position of first nonzero provides a[n] belonging to 2n-1 odd number.

MATHEMATICA

Needs["CNT`"]; Table[m=1; While[PhiInverse[n*2^m] == {}, m++], {n, 1, 200, 2}]

CROSSREFS

Similar to but different from A046067. See also A058887, A057192.

Cf. A000010, A002202, A007617, A046067, A058887, A057192.

Sequence in context: A268679 A128807 A309035 * A033809 A046067 A305531

Adjacent sequences:  A071625 A071626 A071627 * A071629 A071630 A071631

KEYWORD

nonn

AUTHOR

Labos Elemer, May 30 2002

STATUS

approved

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Last modified September 17 16:57 EDT 2019. Contains 327136 sequences. (Running on oeis4.)