A373149 Fully additive with a(2) = 1 and a(p) = prevprime(p) for odd primes p.

0, 1, 2, 2, 3, 3, 5, 3, 4, 4, 7, 4, 11, 6, 5, 4, 13, 5, 17, 5, 7, 8, 19, 5, 6, 12, 6, 7, 23, 6, 29, 5, 9, 14, 8, 6, 31, 18, 13, 6, 37, 8, 41, 9, 7, 20, 43, 6, 10, 7, 15, 13, 47, 7, 10, 8, 19, 24, 53, 7, 59, 30, 9, 6, 14, 10, 61, 15, 21, 9, 67, 7, 71, 32, 8, 19, 12, 14, 73, 7, 8, 38, 79, 9, 16, 42, 25, 10, 83, 8, 16

Offset: 1

Author

Antti Karttunen, Jun 02 2024

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16384
• Index entries for sequences related to prime indices in the factorization of n

Crossrefs

Cf. A064989, A151799.

Cf. also A001414, A059975, A276085.

Programs

Mathematica

A373149[n_] := If[n == 1, 0, Total[MapApply[#2*If[# == 2, 1, NextPrime[#, -1]] &, FactorInteger[n]]]];
Array[A373149, 100] (* Paolo Xausa, Dec 17 2024 *)

PARI

A373149(n) = { my(f = factor(n)); sum(i = 1, #f~, f[i, 2]*if(2==f[i, 1], 1, precprime(f[i, 1] - 1))); };

Formula

Additive with a(p^e) = e*A064989(p).