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A348279 a(n) = Sum_{d|n} d*d', where d' is the arithmetic derivative of d (A003415). 2
0, 2, 3, 18, 5, 35, 7, 114, 57, 77, 11, 243, 13, 135, 128, 626, 17, 467, 19, 573, 220, 299, 23, 1395, 255, 405, 786, 1047, 29, 1160, 31, 3186, 476, 665, 432, 2835, 37, 819, 640, 3389, 41, 2100, 43, 2427, 1937, 1175, 47, 7283, 693, 2577, 1040, 3333, 53, 5570, 896, 6295, 1276 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
LINKS
FORMULA
a(p) = p for primes p since we have a(p) = 1*1' + p*p' = 1*0 + p*1 = p.
a(n) = Sum_{d|n} A190116(d). - Antti Karttunen, Dec 07 2021
EXAMPLE
a(4) = 18; a(4) = 1*1' + 2*2' + 4*4' = 1*0 + 2*1 + 4*4 = 18.
PROG
(PARI) ad(n) = vecsum([n/f[1]*f[2]|f<-factor(n+!n)~]); \\ A003415
a(n) = sumdiv(n, d, d*ad(d)); \\ Michel Marcus, Oct 10 2021
CROSSREFS
Cf. A003415 (arithmetic derivative).
Inverse Möbius transform of A190116.
Cf. also A347130.
Sequence in context: A073524 A130226 A287621 * A344530 A328624 A328627
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, Oct 09 2021
STATUS
approved

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Last modified April 18 16:22 EDT 2024. Contains 371780 sequences. (Running on oeis4.)