login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A253629 Multiplicative function defined for prime powers by a(p^e) = p^(e-1)(p+1) if p > 2 and a(2^e) = 2^(e-1). 2
1, 1, 4, 2, 6, 4, 8, 4, 12, 6, 12, 8, 14, 8, 24, 8, 18, 12, 20, 12, 32, 12, 24, 16, 30, 14, 36, 16, 30, 24, 32, 16, 48, 18, 48, 24, 38, 20, 56, 24, 42, 32, 44, 24, 72, 24, 48, 32, 56, 30, 72, 28, 54, 36, 72, 32, 80, 30, 60, 48, 62, 32, 96, 32, 84, 48, 68, 36, 96, 48, 72, 48, 74, 38, 120, 40, 96, 56, 80, 48, 108, 42, 84, 64, 108, 44, 120, 48, 90, 72, 112, 48 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

a(1) is put to 1.

a(n) = A001615(n) if n is odd and a(n) = A001615(n)/3 if n is even.

This arithmetic function is a sort of modification of the Dedekind psi function (A001615). This modification is made in order to construct the additive arithmetic function A253630.

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..1000

Colin Defant, An arithmetic function arising from the Dedekind psi function, arXiv:1501.00971 [math.NT], 2015.

MAPLE

seq(x * mul(`if`(p>2, p+1, 1)/p, p=numtheory:-factorset(x)), x = 1..100);

# Robert Israel, Jan 08 2015

MATHEMATICA

Table[If[EvenQ[n], (1/3) If[n > 1, n Times @@ (1 + 1/(Select[Divisors[n], PrimeQ])), 1], If[n > 1, n Times @@ (1 + 1/(Select[Divisors[n], PrimeQ])), 1]], {n, 260}]

PROG

(PARI) a(n)=my(f=factor(n)); prod(i=1, #f~, f[i, 1]^(f[i, 2]-1)*if(f[i, 1]>2, f[i, 1]+1, 1)) \\ Charles R Greathouse IV, Jan 08 2015

CROSSREFS

Cf. A001615 (Dedekind psi function).

Sequence in context: A161912 A162339 A200697 * A327095 A176836 A021705

Adjacent sequences:  A253626 A253627 A253628 * A253630 A253631 A253632

KEYWORD

nonn,mult

AUTHOR

Colin Defant, Jan 06 2015

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified September 15 12:22 EDT 2019. Contains 327078 sequences. (Running on oeis4.)