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 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

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Last modified February 26 09:37 EST 2020. Contains 332277 sequences. (Running on oeis4.)