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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.
6
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, 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, 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
OFFSET
1,4
FORMULA
a(n) = Sum_{d|n, d<n} A276150(d).
a(n) = A319715(n) - A276150(n).
MATHEMATICA
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 *)
PROG
(PARI)
A276150(n) = { my(s=0, p=2, d); while(n, d = (n%p); s += d; n = (n-d)/p; p = nextprime(1+p)); (s); };
A319713(n) = sumdiv(n, d, (d<n)*A276150(d));
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Antti Karttunen, Oct 02 2018
STATUS
approved