login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A126254 Number of distinct terms i^j for 1 <= i,j <= n. 5
1, 3, 7, 11, 19, 28, 40, 50, 60, 76, 96, 115, 139, 163, 189, 207, 239, 270, 306, 340, 378, 417, 461, 503, 539, 585, 621, 670, 726, 779, 839, 881, 941, 1003, 1067, 1113, 1185, 1254, 1326, 1397, 1477, 1553, 1637, 1717, 1799, 1884, 1976, 2063, 2135, 2225 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

An easy upper bound is n(n-1)+1 = A002061(n).

LINKS

N. Hobson and John Silberholz, Table of n, a(n) for n = 1..10000 [Terms 1 through 1000 were computed by N. Hobson; terms 1001 through 10000 by John Silberholz, Feb 23 2015]

N. Hobson, Home page (listed in lieu of email address)

John Silberholz, Combinatorial approach to calculate sequence

EXAMPLE

a(4) = 11, as there are 11 distinct terms in 1^1=1, 1^2=1, 1^3=1, 1^4=1, 2^1=2, 2^2=4, 2^3=8, 2^4=16, 3^1=3, 3^2=9, 3^3=27, 3^4=81, 4^1=4, 4^2=16, 4^3=64, 4^4=256.

MAPLE

seq(nops({seq(seq(i^j, i=1..n), j=1..n)}), n=1..100); # Robert Israel, Feb 23 2015

PROG

(PARI) lim=50; z=listcreate(lim*(lim-1)+1); for(m=1, lim, for(i=1, m, x=factor(i); x[, 2]*=m; s=Str(x); f=setsearch(z, s, 1); if(f, listinsert(z, s, f))); t=factor(m); for(j=1, m, x=t; x[, 2]=j*t[, 2]; s=Str(x); f=setsearch(z, s, 1); if(f, listinsert(z, s, f))); print1(#z, ", "))

(R) A126254 <- function(limit) {  if (limit == 1) { return(1) } ; num.powers <- c(1, rep(0, limit-1)) ; handled <- c(T, rep(F, limit-1)) ; for (base in 2:ceiling(sqrt(limit))) { if (!handled[base]) { num.handle <- floor(log(limit, base)) ; handled[base^(1:num.handle)] <- T ; num.powers[base] <- length(unique(as.vector(outer(1:num.handle, 1:limit)))) }} ; num.powers[!handled] <- limit ; sum(num.powers) } ; A126254(50) # John Silberholz, Feb 23 2015

CROSSREFS

Cf. A027424, A061786, A126255, A126256, A126257.

Sequence in context: A292095 A265323 A276456 * A092102 A158722 A202301

Adjacent sequences:  A126251 A126252 A126253 * A126255 A126256 A126257

KEYWORD

easy,nonn

AUTHOR

Nick Hobson, Dec 24 2006

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 July 5 07:37 EDT 2020. Contains 335462 sequences. (Running on oeis4.)