A334341 - OEIS

A334341

a(n) = Sum_{p|n, p prime} (n - p).

0, 0, 0, 2, 0, 7, 0, 6, 6, 13, 0, 19, 0, 19, 22, 14, 0, 31, 0, 33, 32, 31, 0, 43, 20, 37, 24, 47, 0, 80, 0, 30, 52, 49, 58, 67, 0, 55, 62, 73, 0, 114, 0, 75, 82, 67, 0, 91, 42, 93, 82, 89, 0, 103, 94, 103, 92, 85, 0, 170, 0, 91, 116, 62, 112, 182, 0, 117, 112, 196, 0, 139, 0, 109

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OFFSET

1,4

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..20000

FORMULA

a(n) = n*omega(n) - sopf(n), where omega is the number of distinct prime factors of n (A001221) and sopf is the sum of the distinct prime factors of n (A008472).

MATHEMATICA

Table[Sum[(n - i)*(PrimePi[i] - PrimePi[i - 1]) (1 - Ceiling[n/i] + Floor[n/i]), {i, n}], {n, 80}]

PROG

(PARI) A334341(n) = if(1==n, 0, my(f=factor(n)); sum(i=1, #f~, n-f[i, 1])); \\ Antti Karttunen, Jan 22 2025

CROSSREFS

Cf. A001221 (omega), A008472 (sopf).

Sequence in context: A340367 A340197 A340140 * A285174 A269430 A363891

Adjacent sequences: A334338 A334339 A334340 * A334342 A334343 A334344

KEYWORD

nonn,easy

AUTHOR

Wesley Ivan Hurt, Sep 09 2020

STATUS

approved