cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-1 of 1 results.

A365473 Odd semiprimes p*q such that A000120(p)*A000120(q) = A000120(p*q).

Original entry on oeis.org

15, 51, 85, 95, 111, 119, 123, 187, 219, 221, 335, 365, 411, 447, 485, 511, 629, 655, 685, 697, 771, 831, 879, 959, 965, 1011, 1139, 1241, 1285, 1405, 1535, 1563, 1649, 1731, 1779, 1799, 1923, 1983, 2005, 2019, 2031, 2045, 2227, 2605, 2735, 2815, 2827, 2885, 3099, 3183, 3279, 3281, 3291, 3327
Offset: 1

Views

Author

Robert Israel, Sep 04 2023

Keywords

Comments

If p is an odd prime < 2^m and A365475(m) exists, then p * A365475(m) is a term. Thus, if A365475 is infinite, this sequence contains infinitely many multiples of every odd prime.

Examples

			a(3) = 85 is a term because 85 = 5 * 17 is an odd semiprime with A000120(5) * A000120(17) = 2 * 2 = 4 = A000120(85).
		

Crossrefs

Intersection of A001358 and A235040, and intersection of A001358 and A365451.

Programs

  • Maple
    g:= proc(n) convert(convert(n,base,2),`+`) end proc:
    N:= 10^4: # for terms <= N
    S:= NULL: p:= 2:
    while 3*p <= N do
      p:= nextprime(p);
      t:= g(p);
      q:= 2:
      do
        q:= nextprime(q);
        if q = p or q*p > N then break fi;
        if g(q)*t = g(p*q) then S:= S, p*q fi;
    od od:
    sort([S]);
Showing 1-1 of 1 results.