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 A338038 a(n) is the sum of the primes and exponents in the prime factorization of n, but ignoring 1-exponents. 5
 0, 2, 3, 4, 5, 5, 7, 5, 5, 7, 11, 7, 13, 9, 8, 6, 17, 7, 19, 9, 10, 13, 23, 8, 7, 15, 6, 11, 29, 10, 31, 7, 14, 19, 12, 9, 37, 21, 16, 10, 41, 12, 43, 15, 10, 25, 47, 9, 9, 9, 20, 17, 53, 8, 16, 12, 22, 31, 59, 12, 61, 33, 12, 8, 18, 16, 67, 21, 26, 14, 71, 10 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS First differs from A106492 for n=64. LINKS Robert Israel, Table of n, a(n) for n = 1..10000 Daniel Tsai, A recurring pattern in natural numbers of a certain property, arXiv:2010.03151 [math.NT], 2020. FORMULA a(n) = A008474(n) for powerful numbers (A001694). EXAMPLE For n = 18 = 2*3^2, a(18) = 2 + (3+2) = 7. MAPLE f:= proc(n) local t;   add(t[1]+t[2], t=subs(1=0, ifactors(n)[2])); end proc: map(f, [\$1..100]); # Robert Israel, Oct 13 2020 MATHEMATICA a[1] = 0; a[n_] := Plus @@ First /@ (f = FactorInteger[n]) + Plus @@ Select[Last /@ f, # > 1 &]; Array[a, 100] (* Amiram Eldar, Oct 08 2020 *) PROG (PARI) a(n) = my(f=factor(n)); vecsum(f[, 1]) + sum(k=1, #f~, if (f[k, 2]!=1, f[k, 2])); CROSSREFS Cf. A008474, A001694, A106492, A338039. Sequence in context: A029908 A081758 A106492 * A112264 A118503 A086295 Adjacent sequences:  A338035 A338036 A338037 * A338039 A338040 A338041 KEYWORD nonn AUTHOR Michel Marcus, Oct 08 2020 STATUS approved

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Last modified July 28 19:33 EDT 2021. Contains 346335 sequences. (Running on oeis4.)