A239245 Composite integers m such that the sum of the integers x <= m not coprime to m ends with digits of m.

240, 5625, 40625, 1640625, 4140625, 39495680, 47265625, 56640625, 3574214656, 66247700480, 115760971776, 233469644963840, 1298980712890625, 6544914573295616, 6233428515519201280

Offset

1,1

Comments

In other words, number m/2*(m+1-phi(m)) ends with digits of m.

Primes form trivial solutions. In fact, for a prime p, we have that phi(p) = p-1 and p/2*(p+1-(p-1)) = p.

a(16) > 10^20. - Max Alekseyev, Dec 19 2024

Links

Table of n, a(n) for n=1..15.

Example

For m = 240, we have phi(240) = 64 and 240/2*(241-64) = 21240 ends with 240.

Maple

with(numtheory); P:=proc(q) local a, b, n;
for n from 1 to q do a:=n; b:=0; while a>0 do b:=b+1; a:=trunc(a/10); od;
if n=(((n/2*(n+1-phi(n))) mod 10^b) then print(n); fi; od; end: P(10^9);

Crossrefs

Cf. A000010, A239244.

Sequence in context: A249533 A324070 A145094 * A218131 A268637 A264317

Adjacent sequences: A239242 A239243 A239244 * A239246 A239247 A239248

Keyword

nonn,more,base

Author

Paolo P. Lava, Mar 13 2014

Extensions

a(6)-a(11) from Giovanni Resta, Mar 14 2014

Edited and a(12)-a(15) added by Max Alekseyev, Dec 15 2024

Status

approved