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A125073 a(n) = sum of the exponents in the prime-factorization of n which are triangular numbers. 3
0, 1, 1, 0, 1, 2, 1, 3, 0, 2, 1, 1, 1, 2, 2, 0, 1, 1, 1, 1, 2, 2, 1, 4, 0, 2, 3, 1, 1, 3, 1, 0, 2, 2, 2, 0, 1, 2, 2, 4, 1, 3, 1, 1, 1, 2, 1, 1, 0, 1, 2, 1, 1, 4, 2, 4, 2, 2, 1, 2, 1, 2, 1, 6, 2, 3, 1, 1, 2, 3, 1, 3, 1, 2, 1, 1, 2, 3, 1, 1, 0, 2, 1, 2, 2, 2, 2, 4, 1, 2, 2, 1, 2, 2, 2, 1, 1, 1, 1, 0, 1, 3, 1, 4, 3 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,6

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..10000

Index entries for sequences computed from exponents in factorization of n

FORMULA

Additive with a(p^e) = A010054(e)*e. - Antti Karttunen, Jul 08 2017

EXAMPLE

The prime-factorization of 360 is 2^3 *3^2 *5^1. There are two exponents in this factorization which are triangular numbers, 1 and 3. So a(360) = 1 + 3 = 4.

MATHEMATICA

f[n_] := Plus @@ Select[Last /@ FactorInteger[n], IntegerQ[Sqrt[8# + 1]] &]; Table[f[n], {n, 110}] (* Ray Chandler, Nov 19 2006 *)

PROG

(PARI)

A010054(n) = issquare(8*n + 1); \\ This function from Michael Somos, Apr 27 2000.

A125073(n) = vecsum(apply(e -> (A010054(e)*e), factorint(n)[, 2])); \\ Antti Karttunen, Jul 08 2017

CROSSREFS

Cf. A010054, A125072, A125030, A125071.

Sequence in context: A147654 A321377 A071467 * A325310 A308881 A281488

Adjacent sequences:  A125070 A125071 A125072 * A125074 A125075 A125076

KEYWORD

nonn

AUTHOR

Leroy Quet, Nov 18 2006

EXTENSIONS

Extended by Ray Chandler, Nov 19 2006

STATUS

approved

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Last modified March 6 03:35 EST 2021. Contains 341841 sequences. (Running on oeis4.)