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 A248030 Least positive integer m such that m + n divides sigma(m)*phi(n), where sigma(.) and phi(.) are given by A000203 and A000010. 3
 2, 12, 4, 2, 3, 6, 2, 10, 3, 2, 21, 8, 3, 22, 13, 8, 9, 6, 8, 12, 3, 8, 10, 4, 5, 10, 21, 8, 20, 26, 4, 8, 7, 14, 13, 12, 8, 4, 33, 8, 23, 6, 20, 12, 3, 16, 22, 72, 7, 10, 13, 4, 27, 42, 5, 24, 15, 26, 57, 18, 11, 38, 27, 20, 31, 4, 21, 36, 19, 2 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Conjecture: a(n) < 2*n for any n > 2. Numbers n such that a(n) > n: 1, 2, 3, 8, 11, 14, 48, 227, 908, 4478, ... The next number, if it exists, is greater than 10^5. - Derek Orr, Sep 29 2014 LINKS Zhi-Wei Sun, Table of n, a(n) for n = 1..10000 EXAMPLE a(2) = 12 since 12 + 2 = 14 divides sigma(12)*phi(2) = 28. MATHEMATICA Do[m=1; Label[aa]; If[Mod[DivisorSigma[1, m]*EulerPhi[n], m+n]==0, Print[n, " ", m]; Goto[bb]]; m= m+1; Goto[aa]; Label[bb]; Continue, {n, 1, 70}] lpim[n_]:=Module[{m=1, ephn=EulerPhi[n]}, While[Mod[ephn*DivisorSigma[1, m], m+n]!=0, m++]; m]; Array[lpim, 70] (* Harvey P. Dale, Feb 14 2024 *) PROG (PARI) a(n)=m=1; while((eulerphi(n)*sigma(m))%(m+n), m++); m vector(100, n, a(n)) \\ Derek Orr, Sep 29 2014 CROSSREFS Cf. A000010, A000203, A248004, A248007, A248008, A248029. Sequence in context: A317206 A164869 A347408 * A082292 A248588 A332350 Adjacent sequences: A248027 A248028 A248029 * A248031 A248032 A248033 KEYWORD nonn AUTHOR Zhi-Wei Sun, Sep 29 2014 STATUS approved

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Last modified September 18 03:51 EDT 2024. Contains 375995 sequences. (Running on oeis4.)