A347047 Smallest squarefree semiprime whose prime indices sum to n.

6, 10, 14, 21, 26, 34, 38, 46, 58, 62, 74, 82, 86, 94, 106, 118, 122, 134, 142, 146, 158, 166, 178, 194, 202, 206, 214, 218, 226, 254, 262, 274, 278, 298, 302, 314, 326, 334, 346, 358, 362, 382, 386, 394, 398, 422, 446, 454, 458, 466, 478, 482, 502, 514, 526

Offset

3,1

Comments

Compared to A001747, we have 21 instead of 22 and lack 2 and 4.

Compared to A100484 (shifted) we have 21 instead of 22 and lack 4.

Compared to A161344, we have 21 instead of 22 and lack 4 and 8.

Compared to A339114, we have 11 instead of 9 and lack 4.

A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798.

A squarefree semiprime (A006881) is a product of any two distinct prime numbers.

Links

Table of n, a(n) for n=3..57.

Example

The initial terms and their prime indices:
    6: {1,2}
   10: {1,3}
   14: {1,4}
   21: {2,4}
   26: {1,6}
   34: {1,7}
   38: {1,8}
   46: {1,9}

Mathematica

Table[Min@@Select[Table[Times@@Prime/@y, {y, IntegerPartitions[n, {2}]}], SquareFreeQ], {n, 3, 50}]

Prog

(Python)
from sympy import prime, sieve
def a(n):
    p = [0] + list(sieve.primerange(1, prime(n)+1))
    return min(p[i]*p[n-i] for i in range(1, (n+1)//2))
print([a(n) for n in range(3, 58)]) # Michael S. Branicky, Sep 05 2021

Crossrefs

The opposite version (greatest instead of smallest) is A332765.

These are the minima of rows of A338905.

The nonsquarefree version is A339114 (opposite: A339115).

A001358 lists semiprimes (squarefree: A006881).

A024697 adds up semiprimes by weight (squarefree: A025129).

A056239 adds up prime indices, row sums of A112798.

A246868 gives the greatest squarefree number whose prime indices sum to n.

A320655 counts factorizations into semiprimes (squarefree: A320656).

A338898, A338912, A338913 give the prime indices of semiprimes.

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

A339116 groups squarefree semiprimes by greater factor, sums A339194.

A339362 adds up prime indices of squarefree semiprimes.

Cf. A001221, A087112, A089994, A098350, A176504, A338900, A338901, A338904, A338907/A338908, A339005, A339191.

Sequence in context: A315224 A315225 A068014 * A057885 A315226 A315227

Adjacent sequences: A347044 A347045 A347046 * A347048 A347049 A347050

Keyword

nonn

Author

Gus Wiseman, Aug 22 2021

Status

approved