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 A331415 Sum of prime factors minus sum of prime indices of n. 13
 0, 1, 1, 2, 2, 2, 3, 3, 2, 3, 6, 3, 7, 4, 3, 4, 10, 3, 11, 4, 4, 7, 14, 4, 4, 8, 3, 5, 19, 4, 20, 5, 7, 11, 5, 4, 25, 12, 8, 5, 28, 5, 29, 8, 4, 15, 32, 5, 6, 5, 11, 9, 37, 4, 8, 6, 12, 20, 42, 5, 43, 21, 5, 6, 9, 8, 48, 12, 15, 6, 51, 5, 52, 26, 5, 13, 9, 9 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS 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. LINKS FORMULA Totally additive with a(prime(k)) = prime(k) - k = A014689(k). a(n) = A001414(n) - A056239(n). EXAMPLE The prime factors of 12 are {2,2,3}, while the prime indices are {1,1,2}, so a(12) = 7 - 4 = 3. MATHEMATICA Table[Total[Cases[If[n==1, {}, FactorInteger[n]], {p_, k_}:>k*(p-PrimePi[p])]], {n, 30}] CROSSREFS The number of k's is A331387(k) = sum of k-th column of A331385. The sum of prime factors of n is A001414(n). The sum of prime indices of n is A056239(n). Numbers divisible by the sum of their prime factors are A036844. Sum of prime factors is divisible by sum of prime indices: A331380 Product of prime indices equals sum of prime factors: A331384. Cf. A000040, A000720, A001222, A014689, A056239, A112798, A301987, A318995, A325036, A330953, A331378, A331379, A331416, A331418. Sequence in context: A128219 A238969 A238956 * A295511 A116505 A110534 Adjacent sequences:  A331412 A331413 A331414 * A331416 A331417 A331418 KEYWORD nonn AUTHOR Gus Wiseman, Jan 17 2020 STATUS approved

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Last modified September 20 11:25 EDT 2020. Contains 337264 sequences. (Running on oeis4.)