A147580 Numbers with exactly 7 distinct odd prime divisors {3,5,7,11,13,17,19}.

4849845, 14549535, 24249225, 33948915, 43648605, 53348295, 63047985, 72747675, 82447365, 92147055, 101846745, 121246125, 130945815, 160044885, 169744575, 189143955, 218243025, 237642405, 247342095, 266741475, 276441165, 305540235, 315239925, 363738375, 373438065

Offset

1,1

Comments

Numbers k such that phi(k)/k = m

( Family of sequences for successive n odd primes )

m=2/3 numbers with exactly 1 distinct prime divisor {3} see A000244

m=8/15 numbers with exactly 2 distinct prime divisors {3,5} see A033849

m=16/35 numbers with exactly 3 distinct prime divisors {3,5,7} see A147576

m=32/77 numbers with exactly 4 distinct prime divisors {3,5,7,11} see A147577

m=384/1001 numbers with exactly 5 distinct prime divisors {3,5,7,11,13} see A147578

m=6144/17017 numbers with exactly 6 distinct prime divisors {3,5,7,11,13,17} see A147579

m=3072/323323 numbers with exactly 7 distinct prime divisors {3,5,7,11,13,17,19} see A147580

m=110592/323323 numbers with exactly 8 distinct prime divisors {3,5,7,11,13,17,19,23} see A147581

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Formula

Sum_{n>=1} 1/a(n) = 1/1658880. - Amiram Eldar, Dec 22 2020

Mathematica

a = {}; Do[If[EulerPhi[4849845 x] == 1658880 x, AppendTo[a, 4849845 x]], {x, 1, 100}]; a

Prog

(Python)
from sympy import integer_log
from oeis_sequences.OEISsequences import bisection
def A147580(n):
    ptuple = (3, 5, 7, 11, 13, 17, 19)
    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 integer_log(x, 3)[0]
    return bisection(lambda x: n+x-g(x, 6), 4849845*n, 4849845*n) # Chai Wah Wu, Mar 18 2026

Crossrefs

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

Sequence in context: A043637 A232676 A361075 * A043662 A125834 A178293

Adjacent sequences: A147577 A147578 A147579 * A147581 A147582 A147583

Keyword

nonn

Author

Artur Jasinski, Nov 07 2008

Extensions

More terms from Amiram Eldar, Mar 11 2020

Status

approved