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 A306360 Numbers k such that A101337(k)/k is an integer. 7
 1, 2, 3, 4, 5, 6, 7, 8, 9, 153, 370, 371, 407, 459, 1634, 8208, 9474, 13598, 48495, 54748, 92727, 93084, 119564, 174961, 306979, 548834, 1741725, 3194922, 4210818, 9800817, 9926315, 12720569, 24678050, 24678051, 88593477, 144688641, 146511208 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS A005188 is a subsequence of this sequence. Sequence is finite. In particular, a(n) < 10^60. If k >= 10^60, then A101337(k) < k. - Chai Wah Wu, Feb 26 2019 LINKS Giovanni Resta, Table of n, a(n) for n = 1..109 (full sequence, first 56 terms from Chai Wah Wu) Barry Fagin, Idempotent Factorizations of Square-free Integers, Preprints (2019). EXAMPLE For k = 1, (1^1)/1 = 1; for k = 459, (4^3 + 5^3 + 9^3) / 459 = 2. MATHEMATICA Select[Range[10^6], IntegerQ[Total[IntegerDigits[#]^IntegerLength[#]]/#] &] (* Michael De Vlieger, Aug 01 2019 *) PROG (PARI) isok(n) = frac(A101337(n)/n) == 0; \\ Michel Marcus, Feb 11 2019 (PARI) select( is(n)=!(A101337(n)%n), [0..999]) \\ M. F. Hasler, Nov 17 2019 (Python) A306360_list, k = [], 1 while k < 10**9:     s = str(k)     l, c = len(s), 0     for i in range(l):         c = (c + int(s[i])**l) % k     if c == 0:         A306360_list.append(k)     k += 1 # Chai Wah Wu, Feb 26 2019 CROSSREFS Cf. A005188, A101337, A306354, A306361. Sequence in context: A001104 A151544 A032561 * A023052 A005188 A032569 Adjacent sequences:  A306357 A306358 A306359 * A306361 A306362 A306363 KEYWORD nonn,base,fini,full AUTHOR Ctibor O. Zizka, Feb 10 2019 EXTENSIONS a(22)-a(37) from Daniel Suteu, Feb 10 2019 STATUS approved

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Last modified February 23 21:20 EST 2020. Contains 332195 sequences. (Running on oeis4.)