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A335403
If n = Product_{i=1..k} p_i^e_i then a(n) = Sum_{i=1..k} e_i * prime(p_i).
0
0, 3, 5, 6, 11, 8, 17, 9, 10, 14, 31, 11, 41, 20, 16, 12, 59, 13, 67, 17, 22, 34, 83, 14, 22, 44, 15, 23, 109, 19, 127, 15, 36, 62, 28, 16, 157, 70, 46, 20, 179, 25, 191, 37, 21, 86, 211, 17, 34, 25, 64, 47, 241, 18, 42, 26, 72, 112, 277, 22, 283, 130, 27, 18
OFFSET
1,2
COMMENTS
Totally additive with a(p) = prime(p) for p prime.
EXAMPLE
The prime factors of 18 are 2 * 3 * 3, so a(18) = prime(2) + prime(3) + prime(3) = 13.
MATHEMATICA
Table[Total[Cases[FactorInteger[n], {p_, k_}:>k*Prime[p]]], {n, 30}]
PROG
(PARI) a(n) = my(f=factor(n)); sum(k=1, #f~, prime(f[k, 1])*f[k, 2]); \\ Michel Marcus, Jun 07 2020
CROSSREFS
Partitions into prime parts are A000607.
Sum of prime factors is A001414.
Primes of prime index are A006450.
Sum of prime indices is A056239.
The multiplicative version is A064988.
Products of primes of prime index are A076610.
Numbers whose prime indices are not all prime are A330945.
Sequence in context: A115059 A250218 A092835 * A327433 A358866 A167522
KEYWORD
nonn,look
AUTHOR
Gus Wiseman, Jun 06 2020
EXTENSIONS
Edited by N. J. A. Sloane, Jun 20 2020 following a suggestion from Bernard Schott.
STATUS
approved