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A062071 a(n) = [n/1] + [n/(2^2)] + [n/(3^3)] + [n/(4^4)] + ... + [n/(k^k)] + ..., up to infinity, where [ ] is the floor function. 3
1, 2, 3, 5, 6, 7, 8, 10, 11, 12, 13, 15, 16, 17, 18, 20, 21, 22, 23, 25, 26, 27, 28, 30, 31, 32, 34, 36, 37, 38, 39, 41, 42, 43, 44, 46, 47, 48, 49, 51, 52, 53, 54, 56, 57, 58, 59, 61, 62, 63, 64, 66, 67, 69, 70, 72, 73, 74, 75, 77, 78, 79, 80, 82, 83, 84, 85, 87, 88, 89, 90 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Seiichi Manyama, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Harry J. Smith)

Vaclav Kotesovec, Plot of a(n)/n for n = 1..100000

FORMULA

a(n) = Sum_{i=1..n} floor(n/i^i). - Wesley Ivan Hurt, Sep 15 2017

G.f.: (1/(1 - x)) * Sum_{k>=1} x^(k^k)/(1 - x^(k^k)). - Seiichi Manyama, Aug 30 2021

Conjecture: a(n) ~ c * n, where c = A073009. - Vaclav Kotesovec, Aug 30 2021

EXAMPLE

a(7) = [7/1] + [7/4] + [7/27] + ... = 7 + 1 + 0 + 0 + ... = 8.

a(8) = [8/1] + [8/4] + [8/27] + [8/256] + ... = 8 + 2 + 0 + 0 + ... = 10.

MATHEMATICA

Flatten[{1, Table[Sum[Floor[n/k^k], {k, 1, Floor[N[Log[n]/LambertW[Log[n]]]] + 1}], {n, 2, 100}]}] (* Vaclav Kotesovec, Aug 30 2021 *)

PROG

(PARI) \p 10 v=[]; for(n=1, 120, v=concat(v, suminf(k=1, floor(n/k^k)))); v

(PARI) for (n=1, 1000, write("b062071.txt", n, " ", suminf(k=1, n\k^k)\1) ) \\ Harry J. Smith, Jul 31 2009

(PARI) a(n)=sum(k=1, exp(lambertw(log(n)))+1, n\k^k) \\ Charles R Greathouse IV, May 28 2015

(SageMath) [sum( floor(n/j^j) for j in (1..1+log(n)) ) for n in (1..100)] # G. C. Greubel, May 06 2022

CROSSREFS

Cf. A006218, A011371, A060832, A347397.

Sequence in context: A039145 A242491 A038129 * A087069 A023737 A037459

Adjacent sequences:  A062068 A062069 A062070 * A062072 A062073 A062074

KEYWORD

nonn,easy

AUTHOR

Amarnath Murthy, Jun 13 2001

EXTENSIONS

More terms from Jason Earls, Jun 21 2001

STATUS

approved

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Last modified May 25 13:50 EDT 2022. Contains 354071 sequences. (Running on oeis4.)