OFFSET
1,2
COMMENTS
Conjecture: The sum of values d*p < m in the definition of the sequence is equal to m for m = 5 only. True for m <= 15000.
A007506 is the subsequence of the prime terms of this sequence. - Amiram Eldar, Jan 20 2022
a(28) > 10^8. - David A. Corneth, Jan 21 2022
LINKS
MATHEMATICA
q[n_] := Module[{ds = Divisors[n], s = 0, r}, Do[r = n/d; ps = Select[Range[2, r], PrimeQ[#] && ! Divisible[n, d*#] &]; s += Total[d*ps], {d, ds}]; Divisible[s, n]]; Select[Range[3000], q] (* Amiram Eldar, Jan 20 2022 *)
PROG
(Python)
import sympy
A350878=[]
for m in range(1, 15001):
sum=0
primes_lessthan_m_by2 = list(sympy.primerange(2, -(m//-2)))
primes_between_m_by2_and_m = list(sympy.primerange(m//2+1, m))
divisors_of_m=sympy.divisors(m, generator=False)
divisors_of_m.remove(m)
if m%2==0:
divisors_of_m.remove(m//2)
for p in primes_between_m_by2_and_m:
sum+=p
for p in primes_lessthan_m_by2:
for d in divisors_of_m:
if p< m//d and m%(d*p)!=0:
sum+=d*p
if sum%m==0:
A350878.append(m)
print(A350878)
(PARI) isok(m) = {my(d=divisors(m), s=0); forprime(p=2, m, for(k=1, #d, my(x=d[k]*p); if ((x < m) && (m % x), s+=x); ); ); (s % m) == 0; } \\ Michel Marcus, Jan 21 2022
(PARI) \\ See Corneth link \\ David A. Corneth, Jan 21 2022
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Devansh Singh, Jan 20 2022
EXTENSIONS
a(16)-a(20) from Amiram Eldar, Jan 21 2022
a(21)-a(27) from David A. Corneth, Jan 21 2022
STATUS
approved