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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A261089 a(n) = least k such that A155043(k) = n; positions of records in A155043. 20
0, 1, 3, 5, 7, 13, 17, 19, 23, 27, 29, 31, 35, 37, 41, 43, 51, 53, 57, 59, 61, 65, 67, 71, 73, 77, 79, 143, 149, 151, 155, 157, 161, 163, 173, 177, 179, 181, 185, 191, 193, 199, 203, 209, 211, 215, 219, 223, 231, 233, 237, 239, 241, 249, 251, 263, 267, 269, 271, 277, 285, 291, 293, 299, 303, 315, 317, 321, 327, 331, 335, 337, 341, 347, 349, 357, 359, 369, 515 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Note that there are even terms besides 0, and they all seem to be squares: a(915) = 7744 (= 88^2), a(41844) = 611524 (= 782^2), a(58264) = 872356 (= 934^2), a(66936) = 1020100 (= 1010^2), a(95309) = 1503076 (= 1226^2), a(105456) = 1653796 (= 1286^2), ...

LINKS

Antti Karttunen, Table of n, a(n) for n = 0..110880

FORMULA

Other identities. For all n >= 0:

A155043(a(n)) = n.

MATHEMATICA

lim = 80; a[0] = 0; a[n_] := a[n] = 1 + a[n - DivisorSigma[0, n]]; t = Table[a@ n, {n, 0, 12 lim}]; Table[First@ Flatten@ Position[t, n] - 1, {n, 0, lim}] (* Michael De Vlieger, Sep 29 2015 *)

PROG

(PARI)

allocatemem(123456789);

uplim = 2162160; \\ = A002182(41).

v155043 = vector(uplim);

v155043[1] = 1; v155043[2] = 1;

for(i=3, uplim, v155043[i] = 1 + v155043[i-numdiv(i)]);

A155043 = n -> if(!n, n, v155043[n]);

n=0; k=0; while(k <= 10000, if(A155043(n)==k, write("b261089.txt", k, " ", n); k++); n++; );

(Scheme, with Antti Karttunen's IntSeq-library, two variants)

(definec (A261089 n) (let loop ((k 0)) (if (= n (A155043 k)) k (loop (+ 1 k)))))

(define A261089 (RECORD-POS 0 0 A155043))

(Haskell)

import Data.List (elemIndex); import Data.Maybe (fromJust)

a261089 = fromJust . (`elemIndex` a155043_list)

-- Reinhard Zumkeller, Nov 27 2015

CROSSREFS

Cf. A000005, A155043, A049820, A259934, A261103.

Cf. A262503 (the last occurrence of n in A155043).

Cf. A262505 (difference between the last and the first occurrence).

Cf. A262507 (the number of occurrences of n in A155043).

Cf also A261085, A261088.

Sequence in context: A188574 A247458 A008996 * A264988 A031163 A106119

Adjacent sequences:  A261086 A261087 A261088 * A261090 A261091 A261092

KEYWORD

nonn

AUTHOR

Antti Karttunen, Sep 23 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 | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified February 22 06:17 EST 2018. Contains 299430 sequences. (Running on oeis4.)