A338910 Numbers of the form prime(x) * prime(y) where x and y are both odd.

4, 10, 22, 25, 34, 46, 55, 62, 82, 85, 94, 115, 118, 121, 134, 146, 155, 166, 187, 194, 205, 206, 218, 235, 253, 254, 274, 289, 295, 298, 314, 334, 335, 341, 358, 365, 382, 391, 394, 415, 422, 451, 454, 466, 482, 485, 514, 515, 517, 527, 529, 538, 545, 554

Offset

1,1

Links

Table of n, a(n) for n=1..54.

Formula

Numbers m such that A001222(m) = A195017(m) = 2. - Peter Munn, Jan 17 2021

Example

The sequence of terms together with their prime indices begins:
      4: {1,1}     146: {1,21}    314: {1,37}
     10: {1,3}     155: {3,11}    334: {1,39}
     22: {1,5}     166: {1,23}    335: {3,19}
     25: {3,3}     187: {5,7}     341: {5,11}
     34: {1,7}     194: {1,25}    358: {1,41}
     46: {1,9}     205: {3,13}    365: {3,21}
     55: {3,5}     206: {1,27}    382: {1,43}
     62: {1,11}    218: {1,29}    391: {7,9}
     82: {1,13}    235: {3,15}    394: {1,45}
     85: {3,7}     253: {5,9}     415: {3,23}
     94: {1,15}    254: {1,31}    422: {1,47}
    115: {3,9}     274: {1,33}    451: {5,13}
    118: {1,17}    289: {7,7}     454: {1,49}
    121: {5,5}     295: {3,17}    466: {1,51}
    134: {1,19}    298: {1,35}    482: {1,53}

Maple

q:= n-> (l-> add(i[2], i=l)=2 and andmap(i->
    numtheory[pi](i[1])::odd, l))(ifactors(n)[2]):
select(q, [$1..1000])[];  # Alois P. Heinz, Nov 23 2020

Mathematica

Select[Range[100], PrimeOmega[#]==2&&OddQ[Times@@PrimePi/@First/@FactorInteger[#]]&]

Prog

(Python)
from math import isqrt
from sympy import primepi, primerange
def A338910(n):
    def bisection(f, kmin=0, kmax=1):
        while f(kmax) > kmax: kmax <<= 1
        kmin = kmax >> 1
        while kmax-kmin > 1:
            kmid = kmax+kmin>>1
            if f(kmid) <= kmid:
                kmax = kmid
            else:
                kmin = kmid
        return kmax
    def f(x): return n+x-sum(primepi(x//p)-a>>1 for a, p in enumerate(primerange(isqrt(x)+1), -1) if a&1)
    return bisection(f, n, n) # Chai Wah Wu, Apr 03 2025

Crossrefs

A338911 is the even instead of odd version.

A339003 is the squarefree case.

A001221 counts distinct prime indices.

A001222 counts prime indices.

A001358 lists semiprimes, with odd/even terms A046315/A100484.

A006881 lists squarefree semiprimes, with odd/even terms A046388/A100484.

A289182/A115392 list the positions of odd/even terms of A001358.

A300912 lists semiprimes with relatively prime indices.

A318990 lists semiprimes with divisible indices.

A338904 groups semiprimes by weight.

A338906/A338907 are semiprimes of even/odd weight.

A338898, A338912, and A338913 give the prime indices of semiprimes, with product A087794, sum A176504, and difference A176506.

A338899, A270650, and A270652 give prime indices of squarefree semiprimes.

A338909 lists semiprimes with non-relatively prime indices.

Cf. A005117, A037143, A055684, A056239, A065516, A112798, A195017, A320655, A320732, A320892, A339004.

Sequence in context: A109885 A054211 A112770 * A392459 A385932 A217514

Adjacent sequences: A338907 A338908 A338909 * A338911 A338912 A338913

Keyword

nonn

Author

Gus Wiseman, Nov 20 2020

Status

approved