A394062 a(n) = A393096(n) - sopf(A393096(n)) where sopf(n) is the sum of distinct primes of n.

2, 3, 7, 13, 13, 19, 31, 31, 43, 43, 67, 73, 103, 139, 157, 163, 193, 193, 211, 229, 211, 283, 313, 379, 367, 439, 433, 409, 541, 571, 613, 643, 613, 691, 571, 757, 823, 829, 859, 883, 967, 1033, 1069, 1063, 1063, 1237, 1291, 1259, 1039, 1399, 1399, 1453, 1453, 1531, 1663, 1669

Offset

1,1

Comments

All terms are prime.

Links

Table of n, a(n) for n=1..56.

Formula

a(n) = A393096(n)-A008472(A393096(n)).

Example

For n=8, a(8) = 31 which added to 13 gives 44.  The distinct primes of 44 are 2 and 11 which sum to 13.

Mathematica

sopf[k_]:=Total[First/@FactorInteger[k]]; q[k_]:=PrimeQ[sopf[k]]&&PrimeQ[k-sopf[k]]; Select[Range[1723], q]-sopf/@Select[Range[1723], q] (* James C. McMahon, Mar 16 2026 *)

Prog

(Python)
from sympy import isprime, primefactors
def ok(n):return isprime(sum(primefactors(n))) and isprime(n-sum(primefactors(n)))
print(list(map(lambda n: n-sum(primefactors(n)), filter(ok, range(1, 2000)))))
(PARI) sopf(k) = vecsum(factor(k)[, 1]); \\ A008472
isok(k) = my(s=sopf(k)); isprime(s) && isprime(k-s); \\ A393096
apply(x->x-sopf(x), select(isok, [1..1000])) \\ Michel Marcus, Mar 09 2026

Crossrefs

Cf. A008472, A394061, A393096.

Sequence in context: A081256 A084955 A273056 * A026472 A286176 A318401

Adjacent sequences: A394059 A394060 A394061 * A394063 A394064 A394065

Keyword

nonn

Author

Guy Siviour, Mar 09 2026

Status

approved