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A359960 Smallest Niven (or Harshad) number (A005349) with exactly n distinct prime factors. 3
1, 2, 6, 30, 210, 2310, 30030, 690690, 14804790, 223092870, 8254436190, 200560490130, 8222980095330, 304250263527210, 13082761331670030, 614889782588491410, 32589158477190044730, 1987938667108592728530, 117288381359406970983270, 7858321551080267055879090 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
a(11) = 200560490130; a(13) = 304250263527210.
a(n) >= A002110(n) = prime(n)#.
Many terms are primorial numbers, see A360011.
LINKS
Giovanni Resta, Harshad numbers.
Eric Weisstein's World of Mathematics, Distinct Prime Factors.
EXAMPLE
2310 = 2*3*5*7*11 is the smallest integer with 5 prime factors because it is a primorial number, as 2310 / (2+3+1+0) = 385, 2310 is a Niven number: a(5) = 2310.
PROG
(PARI) a(n) = my(k=1); while ((k % sumdigits(k)) || (omega(k) != n), k++); k; \\ Michel Marcus, Jan 20 2023
(PARI)
omega_niven(A, B, n) = A=max(A, vecprod(primes(n))); (f(m, p, j) = my(list=List()); forprime(q=p, sqrtnint(B\m, j), my(v=m*q, r=nextprime(q+1)); while(v <= B, if(j==1, if(v>=A && v%sumdigits(v) == 0, listput(list, v)), if(v*r <= B, list=concat(list, f(v, r, j-1)))); v *= q)); list); vecsort(Vec(f(1, 2, n)));
a(n) = if(n==0, return(1)); my(x=vecprod(primes(n)), y=2*x); while(1, my(v=omega_niven(x, y, n)); if(#v >= 1, return(v[1])); x=y+1; y=2*x); \\ Daniel Suteu, Jan 22 2023
CROSSREFS
Similar: A060319 (Fibonacci), A083002 (oblong), A359961 (Zuckerman).
Sequence in context: A233438 A002110 A118491 * A088257 A058694 A336672
KEYWORD
nonn,base
AUTHOR
Bernard Schott, Jan 20 2023
EXTENSIONS
a(8)-a(9) from Michel Marcus, Jan 20 2023
a(10)-a(19) from Daniel Suteu, Jan 22 2023
STATUS
approved

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Last modified April 23 03:30 EDT 2024. Contains 371906 sequences. (Running on oeis4.)