A270815 Let M be the n-th Giuga number (see A007850); a(n) = sum of (M/p - 1)/p for primes p dividing M.

11, 321, 657, 24699, 824438641, 9331106993, 165242994898683, 5626813041698235, 210318566007979643, 90916134718317480897884289, 206287562744685037912181145873, 729990278282182004516138224533969

Offset: 1

Author

Paolo P. Lava, Mar 23 2016

Keywords

• nonn
• more

Comments

For the additional Giuga number (not known to be the next term of A007850), 4200017949707747062038711509670656632404195753751630609228764416142557211582098432545190323474818 the corresponding value is 1563694051115215735786664430977202618214176554388873529993304101116913223541171676954379378709457.

Examples

			Prime factors of 30 are 2, 3 and 5: (30/2 - 1)/2 + (30/3 - 1)/3 + (30/5 - 1)/5 = 7 + 3 + 1 = 11.
		

Crossrefs

Cf. A007850, A270816.

Programs

Maple

with(numtheory): P:=proc(q) local n,x; x:=[30, 858, 1722, 66198, 2214408306, 24423128562, 432749205173838, 14737133470010574, 550843391309130318, 244197000982499715087866346, 554079914617070801288578559178, 1910667181420507984555759916338506];
for n from 1 to nops(x) do print(add((x[n]/k-1)/k,k=factorset(x[n]))); od; end: P(1);