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

1,3

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

Formula

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

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 *)

Prog

(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))); };

Crossrefs

Cf. A064989, A151799.

Cf. also A001414, A059975, A276085.

Sequence in context: A254309 A079375 A069933 * A204987 A102347 A230846

Adjacent sequences: A373146 A373147 A373148 * A373150 A373151 A373152

Keyword

nonn

Author

Antti Karttunen, Jun 02 2024

Status

approved