A147574 Numbers with exactly 7 distinct prime divisors {2,3,5,7,11,13,17}.

510510, 1021020, 1531530, 2042040, 2552550, 3063060, 3573570, 4084080, 4594590, 5105100, 5615610, 6126120, 6636630, 7147140, 7657650, 8168160, 8678670, 9189180, 10210200, 10720710, 11231220, 12252240, 12762750, 13273260, 13783770

Offset

1,1

Comments

Successive numbers k such that EulerPhi(x)/x = m:

( Family of sequences for successive n primes )

m=1/2 numbers with exactly 1 distinct prime divisor {2} see A000079

m=1/3 numbers with exactly 2 distinct prime divisors {2,3} see A033845

m=4/15 numbers with exactly 3 distinct prime divisors {2,3,5} see A143207

m=8/35 numbers with exactly 4 distinct prime divisors {2,3,5,7} see A147571

m=16/77 numbers with exactly 5 distinct prime divisors {2,3,5,7,11} see A147572

m=192/1001 numbers with exactly 6 distinct prime divisors {2,3,5,7,11,13} see A147573

m=3072/17017 numbers with exactly 7 distinct prime divisors {2,3,5,7,11,13,17} see A147574

m=55296/323323 numbers with exactly 8 distinct prime divisors {2,3,5,7,11,13,17,19} see A147575

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Harvey P. Dale)

Formula

a(n) = 510510 * A080681(n). - Amiram Eldar, Mar 10 2020

Sum_{n>=1} 1/a(n) = 1/92160. - Amiram Eldar, Nov 12 2020

Mathematica

a = {}; Do[If[EulerPhi[x 510510] == 92160 x, AppendTo[a, 510510 x]], {x, 1, 100}]; a
sdpdQ[n_]:=Module[{f=FactorInteger[n][[All, 1]]}, Length[f]==7&&Max[f]==17]; Select[Range[510510, 138*10^5, 510510], sdpdQ] (* Harvey P. Dale, Aug 03 2019 *)

Prog

(Python)
from sympy import integer_log
from oeis_sequences.OEISsequences import bisection
def A147574(n):
    ptuple = (2, 3, 5, 7, 11, 13, 17)
    def g(x, m): return sum(g(x//(ptuple[m]**i), m-1) for i in range(1, integer_log(x, ptuple[m])[0]+1)) if m else x.bit_length()-1
    return bisection(lambda x: n+x-g(x, 6), 510510*n, 510510*n) # Chai Wah Wu, Mar 18 2026

Crossrefs

Cf. A060735, A080681, A143207, A147571-A147575, A147576-A147580.

Sequence in context: A176655 A123321 A258362 * A046325 A136352 A138207

Adjacent sequences: A147571 A147572 A147573 * A147575 A147576 A147577

Keyword

nonn

Author

Artur Jasinski, Nov 07 2008

Status

approved