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A319713 Sum of A276150(d) over proper divisors d of n, where A276150 gives the sum of digits in primorial base.

%I A319713 #12 Mar 06 2024 01:00:49
%S A319713 0,1,1,2,1,4,1,4,3,5,1,7,1,4,6,6,1,8,1,10,5,6,1,11,4,5,6,9,1,15,1,10,
%T A319713 7,7,6,15,1,6,6,16,1,15,1,13,13,8,1,19,3,13,8,12,1,17,8,17,7,9,1,24,1,
%U A319713 4,13,12,7,17,1,12,9,17,1,23,1,5,15,11,7,17,1,24,12,7,1,28,9,6,10,19,1,27,6,15,5,8,8,25,1,12,13,24,1,19,1,20,21
%N A319713 Sum of A276150(d) over proper divisors d of n, where A276150 gives the sum of digits in primorial base.
%H A319713 Antti Karttunen, <a href="/A319713/b319713.txt">Table of n, a(n) for n = 1..65537</a>
%H A319713 <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>.
%F A319713 a(n) = Sum_{d|n, d<n} A276150(d).
%F A319713 a(n) = A319715(n) - A276150(n).
%t A319713 d[n_] := Module[{k = n, p = 2, s = 0, r}, While[{k, r} = QuotientRemainder[k, p]; k != 0 || r != 0, s += r; p = NextPrime[p]]; s]; a[n_] := DivisorSum[n, d[#] &, # < n &]; Array[a, 100] (* _Amiram Eldar_, Mar 05 2024 *)
%o A319713 (PARI)
%o A319713 A276150(n) = { my(s=0, p=2, d); while(n, d = (n%p); s += d; n = (n-d)/p; p = nextprime(1+p)); (s); };
%o A319713 A319713(n) = sumdiv(n,d,(d<n)*A276150(d));
%Y A319713 Cf. A276150, A319711, A319715.
%K A319713 nonn,base
%O A319713 1,4
%A A319713 _Antti Karttunen_, Oct 02 2018