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 A262503 a(n) = largest k such that A155043(k) = n. 16
 0, 2, 6, 12, 18, 22, 30, 34, 42, 48, 60, 72, 84, 96, 108, 120, 132, 140, 112, 116, 126, 124, 130, 138, 150, 156, 168, 180, 176, 184, 192, 204, 216, 228, 240, 248, 264, 280, 250, 258, 270, 288, 296, 312, 306, 320, 328, 340, 352, 364, 372, 354, 358, 368, 384, 396, 420, 402, 414, 418, 432, 450, 468, 480, 504, 520, 540, 560, 572, 580, 594, 612, 610, 618, 622, 628, 648, 672, 592 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS The first odd terms occur as a(121) = 1089, a(123) = 1093, a(349) = 3253, a(717) = 7581, a(807) = 8685, a(1225) = 13689, etc. LINKS Antti Karttunen, Table of n, a(n) for n = 0..110880 FORMULA Other identities and observations. For all n >= 0: A262502(n+2) > a(n). [Not rigorously proved, but empirical evidence and common sense agrees.] MATHEMATICA lim = 80; a[0] = 0; a[n_] := a[n] = 1 + a[n - DivisorSigma[0, n]]; t = Table[a@ n, {n, 0, 12 lim}]; Last@ Flatten@ Position[t, #] - 1 & /@ Range[0, lim] (* Uses the product of a limit and an arbitrary coefficient (12) based on observation of output for low values (n < 500). This might need to be adjusted for large n to give correct values of a(n). - Michael De Vlieger, Sep 29 2015 *) (* Note: one really should use a general safe limit, like A262502(n+2) I use in my Scheme-program. - Antti Karttunen, 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]); uplim2 = 110880; \\ = A002182(30). v262503 = vector(uplim2); for(i=1, uplim, if(v155043[i] <= uplim2, v262503[v155043[i]] = i)); A262503 = n -> if(!n, n, v262503[n]); for(n=0, uplim2, write("b262503.txt", n, " ", A262503(n))); (Scheme) (define (A262503 n) (let loop ((k (A262502 (+ 2 n)))) (if (= (A155043 k) n) k (loop (- k 1))))) CROSSREFS Cf. A261089 (gives the first occurrence of n in A155043). Cf. A262507 (gives the number of times n occurs in A155043). Cf. A259934, A262502. Sequence in context: A026229 A259934 A263269 * A263082 A043343 A066080 Adjacent sequences:  A262500 A262501 A262502 * A262504 A262505 A262506 KEYWORD nonn AUTHOR Antti Karttunen, Sep 24 2015 STATUS approved

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Last modified January 20 14:13 EST 2019. Contains 319333 sequences. (Running on oeis4.)