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 A349705 Numbers k such that the concatenation in increasing order of their prime factors, with multiplicity, is congruent to 1 (mod k). 1
 36, 39, 66, 1435, 5714, 6410, 13861, 22564, 27346, 33137, 45542, 79260, 171860, 268218, 442068, 486127, 675423, 2287527, 3710027, 9610766, 14318290, 26293568, 29361702, 49703324, 227358366, 433100023, 442960845, 479174118, 1221238938, 1243718114, 4053362596, 8620689655 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS Martin Ehrenstein, Table of n, a(n) for n = 1..39 EXAMPLE a(3) = 66 is a term because the concatenation of its prime factors is 2311 and 2311 == 1 (mod 66). MAPLE filter:= proc(n) local L, t; lcat(map(t -> t[1]\$t[2], sort( ifactors(n)[2], (a, b) -> a[1] < b[1]))) mod n = 1; end proc: select(filter, [\$1..10^7]); MATHEMATICA upto=10^5; a={}; Do[If[Mod[FromDigits[Flatten[Map[IntegerDigits[ConstantArray[First[#], Last[#]]]&, FactorInteger[k]]]], k]==1, AppendTo[a, k]], {k, upto}]; a (* Paolo Xausa, Nov 26 2021 *) PROG (Python) from sympy import factorint def ok(k): return int("".join(map(str, factorint(k, multiple=True))))%k == 1 print([k for k in range(2, 10**5) if ok(k)]) # Michael S. Branicky, Nov 26 2021 (Python) from itertools import count, islice from sympy import factorint def A349705_gen(startvalue=1): # generator of terms >= startvalue for k in count(max(startvalue, 1)): c = 0 for d in sorted(factorint(k, multiple=True)): c = (c*10**len(str(d)) + d) % k if c == 1: yield k A349705_list = list(islice(A349705_gen(), 10)) # Chai Wah Wu, Feb 28 2022 CROSSREFS Cf. A037276, A259047. Sequence in context: A337861 A261373 A248372 * A129288 A083248 A360765 Adjacent sequences: A349702 A349703 A349704 * A349706 A349707 A349708 KEYWORD nonn,hard AUTHOR J. M. Bergot and Robert Israel, Nov 25 2021 EXTENSIONS a(28)-a(32) from Martin Ehrenstein, Nov 27 2021 STATUS approved

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Last modified August 6 15:42 EDT 2024. Contains 374974 sequences. (Running on oeis4.)