A084622 Numbers n such that f(n) is a strict local extremum for the function f(x) = phi(x) + sigma(x); i.e., either f(n) > f(n-1) and f(n) > f(n+1) or f(n) < f(n-1) and f(n) < f(n+1).

12, 13, 16, 17, 18, 19, 20, 21, 24, 25, 28, 29, 30, 31, 32, 33, 36, 37, 40, 41, 42, 43, 44, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 60, 61, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 76, 77, 78, 79, 80, 84, 85, 88, 89, 90, 91, 92, 93, 96, 97, 100, 101, 102, 103, 104, 108, 109

Offset

1,1

Comments

For runs of consecutive strict local extrema (alternating minima/maxima, zigzags) of f, cf. A066923.

A066485 is an analog of the present sequence for the prime gaps function.

Links

Table of n, a(n) for n=1..67.

Example

16 is a term since f(16) is a local maximum: f(15) = 32, f(16) = 39, f(17) = 34.

Prog

(PARI) f(x)=eulerphi(x)+sigma(x)
{locext(n)=local(a, b, c); a=if(n<2, 0, f(n-1)); b=f(n); c=f(n+1); if(a<b&&b>c, 1, if(a>b&&b<c, -1, 0))}
for(n=1, 110, if(locext(n)!=0, print1(n, ", ")))

Crossrefs

Cf. A066485, A066923.

Sequence in context: A267615 A323032 A003894 * A155147 A246781 A241748

Adjacent sequences: A084619 A084620 A084621 * A084623 A084624 A084625

Keyword

nonn

Author

Klaus Brockhaus, Jun 01 2003

Status

approved