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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A284521 Sum of largest prime power factors of numbers <= n. 1
1, 3, 6, 10, 15, 18, 25, 33, 42, 47, 58, 62, 75, 82, 87, 103, 120, 129, 148, 153, 160, 171, 194, 202, 227, 240, 267, 274, 303, 308, 339, 371, 382, 399, 406, 415, 452, 471, 484, 492, 533, 540, 583, 594, 603, 626, 673, 689, 738, 763, 780, 793, 846, 873, 884, 892, 911, 940, 999, 1004, 1065, 1096, 1105, 1169, 1182 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Partial sums of A034699.

LINKS

Robert Israel, Table of n, a(n) for n = 1..10000

FORMULA

Conjecture: a(n) = O(n^2/log(n)).

EXAMPLE

a(1) = 1;

a(2) = 3 because 2 is a prime and 1 + 2 = 3;

a(3) = 6 because 3 is a prime and 3 + 3 = 6;

a(4) = 10 because 4 = 2^2 and 6 + 4 = 10;

a(5) = 15 because 5 is a prime and 10 + 5 = 15;

a(6) = 18 because 12 = 2*3 and 15 + 3 = 18, etc.

MAPLE

g:= n -> max(map(t -> t[1]^t[2], ifactors(n)[2])): g(1):= 1:

ListTools:-PartialSums(map(g, [$1..100])); # Robert Israel, Mar 29 2017

MATHEMATICA

Accumulate[Join[{1}, Table[Last[Select[Divisors[n], PrimePowerQ[#1] & ]], {n, 2, 65}]]]

PROG

(PARI) a(n) = if (n==1, 1, 1+ sum(k=2, n, f = factor(k); f[#f~, 1]^f[#f~, 2])); \\ Michel Marcus, Mar 28 2017

CROSSREFS

Cf. A034699, A046670, A073355.

Sequence in context: A054731 A282064 A029716 * A162553 A310072 A310073

Adjacent sequences:  A284518 A284519 A284520 * A284522 A284523 A284524

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Mar 28 2017

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 | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 17 12:33 EDT 2018. Contains 316280 sequences. (Running on oeis4.)