A217690 Numbers n such that sum of digits of n equals the least prime dividing n and sum of squares of digits of n equals the greatest prime dividing n.

133, 803, 2023, 106811, 383177, 1071949, 1342027, 2025343, 2569757, 2911123, 3341831, 3993883, 6285901, 10860071, 11194319, 13270013, 21736109, 21871477, 22159451, 22421587, 26011229, 27600257, 31174391, 32656681, 34880611, 40435193, 41755573, 53738911

Offset

1,1

Links

Table of n, a(n) for n=1..28.

Formula

k such that A020639(k) = A007953(k) and A006530(k) = A003132(k).

Example

383177 = 29 * 73 * 181 is in the sequence because 29 = 3+8+3+1+7+7 and 181 = 3^2+8^2+3^2+1^2+7^2+7^2.

Maple

with(numtheory):A:= proc(n) add(u, u=convert(n, base, 10)) ; end proc: B:= proc(m) add(v^2, v=convert(m, base, 10)) ; end proc: for i from 2 to 1000000 do:x:=factorset(i):n1:=nops(x):if x[1]=A(i) and x[n1]=B(i) then print(i):else fi:od:

Prog

(PARI) is_A217690(n)={my(d=digits(n), s=norml2(d), f); (n%s || !isprime(s) || n%(d=sum(i=1, #d, d[i])) || !isprime(d)) & return; !(f=factor(n/(d*s))[, 1]) || (d <= f[1] & s >= f[#f])} \\ Charles R Greathouse IV and M. F. Hasler, Oct 11 2012

Crossrefs

Cf. A007953, A003132, A020639, A006530.

Sequence in context: A137879 A249108 A020237 * A117565 A357489 A274175

Adjacent sequences: A217687 A217688 A217689 * A217691 A217692 A217693

Keyword

nonn,base

Author

Michel Lagneau, Oct 11 2012

Status

approved