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A248568 Least positive integer m such that phi(m+n) divides m, where phi(.) is Euler's totient function. 2
1, 2, 6, 2, 20, 4, 8, 4, 12, 40, 24, 6, 20, 12, 24, 8, 48, 16, 32, 18, 24, 8, 72, 12, 44, 40, 36, 24, 132, 12, 56, 16, 60, 96, 40, 18, 180, 36, 60, 36, 144, 40, 80, 16, 72, 20, 168, 24, 92, 88, 184, 80, 276, 24, 104, 42, 48, 264, 312, 24 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Conjecture: a(n) exists for any n > 0. Moreover, a(n) <= n*(n-1) for all n > 1.

Note that for n > 1 the term a(n) should be even.

LINKS

Zhi-Wei Sun, Table of n, a(n) for n = 1..10000

EXAMPLE

a(10) = 40 since phi(40+10) = 20 divides 40.

MATHEMATICA

Do[m=1; Label[aa]; If[Mod[m, phi[m+n]]==0, Print[n, " ", m]; Goto[bb]]; m=m+1; Goto[aa]; Label[bb]; Continue, {n, 1, 60}]

PROG

(PARI)

a(n)=m=1; while(m%eulerphi(m+n), m++); m

vector(100, n, a(n)) \\ Derek Orr, Oct 08 2014

CROSSREFS

Cf. A000010, A248007, A248058.

Sequence in context: A284436 A322312 A174857 * A257252 A327171 A008556

Adjacent sequences:  A248565 A248566 A248567 * A248569 A248570 A248571

KEYWORD

nonn

AUTHOR

Zhi-Wei Sun, Oct 08 2014

STATUS

approved

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Last modified January 16 16:32 EST 2022. Contains 350376 sequences. (Running on oeis4.)