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 A337839 Numbers that can be written as (k + sum of digits of k) for some k, then as (m + product of digits of m) for some m, also as (q * product of digits of q) for some q, and finally as (t * sum of digits of t) for some t. 1
 4, 16, 81, 88, 144, 250, 520, 900, 1008, 1053, 1134, 2025, 2304, 2655, 3726, 4680, 6408, 6624, 9928, 12024, 12150, 12510, 13608, 14256, 15480, 16408, 17128, 17172, 18304, 19152, 19288, 19602, 23310, 24336, 25110, 26550, 29358, 32896, 32968, 36864, 37485, 38592 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Equivalently, Bogotá numbers that are not Colombian and that can be written as (m + product of digits of m) for some m and also as (t * sum of digits of t) for some t. The only primes that can belong to this sequence are repunits > 11 whose indices are in A004023. It is known that these primes belong to A336983 but do they belong also to A337718 and A337816? Observation: 7 of the first 13 terms are perfect squares: 4, 16, 81, 144, 900, 2025, 2304 (see examples). LINKS Seiichi Manyama, Table of n, a(n) for n = 1..1000 Index to sequences related to Colombian numbers. EXAMPLE 4 = 2 + 2 = 2 + 2 = 2 * 2 = 2 * 2; 16 = 8 + 8 = 8 + 8 = 4 * 4 = 4 * 4; 81 = 72 + (7+2) = 63 + (6*3) = 9 * 9 = 9 * 9; 144 = 135 + (1+3+5) = 128 + (1*2*8) = 18 * (1*8) = 24 * (2+4). MATHEMATICA m = 40000; Select[Intersection @@ Union /@ Transpose[Table[{n + (s = Plus @@ (d = IntegerDigits[n])), n + (p = Times @@ d), n*s, n*p}, {n, 1, m}]], # <= m &] (* Amiram Eldar, Sep 25 2020 *) PROG (PARI) lista(nn) = {my(vd = vector(nn, k, digits(k)), vs = vector(nn, k, vecsum(vd[k])), vp = vector(nn, k, vecprod(vd[k])), vsp = Set(vector(nn, k, k+vp[k])), vss = Set(vector(nn, k, k+vs[k])), vps = Set(vector(nn, k, k*vs[k])), vpp = Set(vector(nn, k, k*vp[k])), vk = vector(nn, k, k)); Vec(setintersect(vk, setintersect(vsp, setintersect(vss, setintersect(vps, vpp))))); } \\ Michel Marcus, Oct 01 2020 CROSSREFS Intersection of A176995, A336826, A337718 and A337816. Intersection of A336983, A337718 and A337816. Intersection of A337733 and A337816. Sequence in context: A002777 A280923 A118997 * A001257 A133053 A342326 Adjacent sequences: A337836 A337837 A337838 * A337840 A337841 A337842 KEYWORD nonn,base AUTHOR Bernard Schott, Sep 25 2020 EXTENSIONS Terms a(7) and beyond from Amiram Eldar, Sep 25 2020 STATUS approved

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Last modified September 10 01:04 EDT 2024. Contains 375769 sequences. (Running on oeis4.)