A351651 a(n) is the quotient obtained when digsum(m^2) is divided by digsum(m), with digsum = sum of digits = A007953 and m = A351650(n).

1, 2, 3, 1, 1, 2, 3, 4, 1, 1, 2, 3, 4, 3, 2, 3, 4, 3, 2, 3, 1, 1, 2, 1, 3, 2, 2, 2, 1, 2, 1, 1, 2, 3, 4, 2, 2, 3, 4, 5, 3, 3, 4, 5, 3, 3, 2, 4, 3, 2, 2, 1, 2, 2, 2, 1, 1, 1, 2, 1, 1, 2, 3, 4, 3, 3, 2, 3, 4, 5, 3, 2, 4, 5, 2, 2, 3, 3, 3, 3, 2, 2, 2, 3, 2, 1, 3, 4, 3, 4, 5

Offset

1,2

Comments

All positive integers are terms of this sequence (see A280012).

a(n) = 1 iff m = A351650(n) is a term of A058369 \ {0}.

a(n) = digsum(n) if m = A351650(n) is a term of A061909 \ {0}.

Links

Table of n, a(n) for n=1..91.

Diophante, A1730 - Des chiffres à sommer pour un entier (in French).

Formula

a(n) = A004159(A351650(n)) / A007953(A351650(n)).

Example

A351650(8) = 13, then digsum(13) = 1+3 = 4 while digsum(13^2) = digsum(169) = 1+6+9 = 16; hence, a(8) = 16/4 = 4.

Mathematica

Select[Total[IntegerDigits[#^2]]/Total[IntegerDigits[#]]& /@ Range[300], IntegerQ] (* Amiram Eldar, Feb 16 2022 *)

Prog

(PARI) lista(nn) = {my(list = List(), q); for (n=1, nn, if (denominator(q=sumdigits(n^2)/sumdigits(n))==1, listput(list, q)); ); Vec(list); } \\ Michel Marcus, Feb 16 2022

Crossrefs

Cf. A002283, A004159, A007953, A058369, A061909, A254066, A280012, A351650.

Sequence in context: A330957 A352924 A327192 * A157813 A111879 A193280

Adjacent sequences: A351648 A351649 A351650 * A351652 A351653 A351654

Keyword

nonn,base

Author

Bernard Schott, Feb 16 2022

Extensions

More terms from Michel Marcus, Feb 16 2022

Status

approved