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

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

1,1

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.

Links

Robert Israel, Table of n, a(n) for n = 1..7230

Example

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

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]);

Crossrefs

Cf. A000120, A365475.

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

Sequence in context: A020144 A339880 A235040 * A075933 A075929 A337295

Adjacent sequences: A365470 A365471 A365472 * A365474 A365475 A365476

Keyword

nonn,base

Author

Robert Israel, Sep 04 2023

Status

approved