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

 

Logo

Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing.
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A143152 A051731 * A020639. 2
1, 3, 4, 5, 6, 8, 8, 7, 7, 10, 12, 12, 14, 12, 12, 9, 18, 13, 20, 14, 14, 16, 24, 16, 11, 18, 10, 16, 30, 20, 32, 11, 18, 22, 18, 19, 38, 24, 20, 18, 42, 22, 44, 20, 18, 28, 48, 20, 15, 17, 24, 22, 54, 18, 22, 20, 26, 34, 60, 28, 62, 36, 20, 13, 24, 26, 68, 26, 30, 26, 72, 25, 74 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

a(n) = (p+1) if n = p.

LINKS

Table of n, a(n) for n=1..73.

FORMULA

Inverse Mobius transform of A020639, where A020639 = Lpf(n): (1, 2, 3, 2, 5, 2, 7, 2, 3, 2, 11,...). Row sums of triangle A143151.

EXAMPLE

a(4) = 5 = (1, 1, 0, 1) dot (1, 2, 3, 2) = (1 + 2 + 0 + 2), where (1, 1, 0, 1) = row 4 of triangle A051731 and A010639 = (1, 2, 3, 2, 5, 2, 7, 2, 3, 2, 11,...).

Since a(n) = sum of least prime factors of the divisors of n, the divisors of 12 are recorded in triangle row 12 of A127093: (1, 2, 3, 4, 0, 6, 0, 0, 0, 0, 0, 12). Lpf of these terms = row 12 of triangle A143151: (1, 2, 3, 2, 0, 2, 0, 0, 0, 0, 0, 2); sum = 12.

MAPLE

read transforms : A020639 := proc(n) local i ; if n = 1 then 1; else for i from 1 do if n mod ithprime(i) = 0 then RETURN(ithprime(i)) ; fi; od: fi; end: a020639 := [seq(A020639(n), n=1..100)] : a143152 := MOBIUSi(a020639) : for i from 1 to nops(a143152) do printf("%d, ", op(i, a143152)) ; od: # R. J. Mathar, Aug 11 2008

CROSSREFS

Cf. A051731, A020639, A127093, A143151.

Sequence in context: A134338 A084919 A153100 * A229109 A096127 A327953

Adjacent sequences:  A143149 A143150 A143151 * A143153 A143154 A143155

KEYWORD

nonn

AUTHOR

Gary W. Adamson, Jul 27 2008

EXTENSIONS

Extended beyond a(14) by R. J. Mathar, Aug 11 2008

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 December 15 04:23 EST 2019. Contains 329991 sequences. (Running on oeis4.)