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 A359959 a(n) is the least number that has exactly n divisors with the same digit sum. 2
 1, 10, 36, 54, 144, 108, 486, 216, 324, 432, 648, 540, 1296, 3510, 2430, 1080, 2700, 1620, 8424, 2160, 4860, 4320, 3240, 27216, 7560, 8100, 6480, 35100, 10800, 19440, 24300, 21060, 15120, 16200, 37800, 56700, 54000, 30240, 42120, 60480, 32400, 45360, 84240, 81000, 64800, 75600, 90720, 213840 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS a(n) is the least number k such that for some s, there are exactly n divisors of k with sum of digits s. LINKS Michael S. Branicky, Table of n, a(n) for n = 1..289 Michael S. Branicky, Table of n, a(n) for all terms <= 446000000 FORMULA a(n) <= 10^(n-1). - Rémy Sigrist, Jan 27 2023 EXAMPLE a(1) = 1 because 1 has 1 divisor with digit sum 1, namely 1. a(2) = 10 because 10 has 2 divisors with digit sum 1, namely 1 and 10. a(3) = 36 because 36 has 3 divisors with digit sum 9, namely 9, 18 and 36. a(4) = 54 because 54 has 4 divisors with digit sum 9, namely 9, 18, 27 and 54. MAPLE f:= proc(n) local L, S; L:= convert(numtheory:-divisors(n), list); S:= map(t -> convert(convert(t, base, 10), `+`), L); map(t -> numboccur(t, S), convert(S, set)) end proc: V:= Vector(50): count:= 0: for n from 1 while count < 50 do for v in f(n) do if v <= 50 and V[v] = 0 then V[v]:= n; count:= count+1; fi od od: convert(V, list); PROG (PARI) is(z, n)={my(e=1, w=[], s=[], t=0); s=vecsort(apply(vecsum, apply(digits, apply(divisors, z)))); for(i=2, #s, if(s[i]==s[i-1], e++, w=concat(w, e); e=1)); w=concat(w, e); s=Set(w); forvec(G=vector(2, j, [1, #s]), if((s[G[1]]==n)&&(s[G[2]]==n), t=1; if(G[1]!=G[2], return(0)))); return(t)} a(n)=for(z=1, +oo, is(z, n)&&return(z)); \\ R. J. Cano, Jan 23 2023 (Python) from sympy import divisors from collections import Counter from itertools import count, islice def sd(n): return sum(map(int, str(n))) def agen(): # generator of terms adict, n = dict(), 1 for k in count(1): c = Counter(sd(d) for d in divisors(k, generator=True)) for v in c.values(): if v >= n and v not in adict: adict[v] = k while n in adict: yield adict[n]; n += 1 print(list(islice(agen(), 50))) # Michael S. Branicky, Jan 27 2023 CROSSREFS Cf. A007953, A359074. Sequence in context: A073613 A346386 A117404 * A309783 A072517 A271912 Adjacent sequences: A359956 A359957 A359958 * A359960 A359961 A359962 KEYWORD nonn,base AUTHOR Robert Israel, Jan 19 2023 STATUS approved

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Last modified April 14 14:16 EDT 2024. Contains 371665 sequences. (Running on oeis4.)