A261089 a(n) = least k such that A155043(k) = n; positions of records in A155043.

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

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: A355424 A339501 A008996 * A264988 A031163 A106119

Adjacent sequences: A261086 A261087 A261088 * A261090 A261091 A261092

Keyword

nonn

Author

Antti Karttunen, Sep 23 2015

Status

approved