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A073815 Least number x such that gcd(phi(x), sigma(x)) = n. 6
1, 3, 18, 12, 200, 14, 3364, 15, 722, 328, 9801, 42, 25281, 116, 1800, 165, 36992, 810, 4414201, 88, 196, 29161, 541696, 35, 2928200, 1413, 103968, 172, 98942809, 488, 1547536, 336, 19602, 17536, 814088, 370, 49042009, 55297, 1521, 319, 3150464641 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Values are frequently identical to terms of A077102. Since gcd(a,b) and gcd(a+b,a-b) may differ, so may the smallest solutions. A077102(m) and a(m) differ at m = 1, 2, 4, 8, 16, 28, 32, 40, etc.

LINKS

Giovanni Resta, Table of n, a(n) for n = 1..120

FORMULA

a(n) = Min{x; A055008(x)=n}. a(n)=Min{x; gcd(A000203(x), A000010(x))=n}

a(n) = Min{x: A023897(x)= n}, smallest balanced number (A020492) for which the quotient equals n.

MATHEMATICA

f[x_] := Apply[GCD, {DivisorSigma[1, x], EulerPhi[x]}] t=Table[0, {100}]; Do[s=f[n]; If[s<101&&t[[s]]==0, t[[s]]=n], {n, 1, 10^13}];

PROG

(PARI) a(n)=my(x=n); while(gcd(eulerphi(x), sigma(x))!=n, x++); x \\ Charles R Greathouse IV, Dec 09 2013

CROSSREFS

Cf. A000203, A000010, A055008, A077099-A077102, A051612, A065387, A023897, A020492.

Sequence in context: A281722 A098874 A077104 * A212994 A307640 A195998

Adjacent sequences:  A073812 A073813 A073814 * A073816 A073817 A073818

KEYWORD

nonn

AUTHOR

Labos Elemer, Nov 12 2002

STATUS

approved

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Last modified July 4 14:51 EDT 2020. Contains 335448 sequences. (Running on oeis4.)